St Andrews Lynx

I think that you need to talk to your advisor about this, and promptly.
You do have evidence at this point: the things that you have told us in the post. Experiments don't work when she is around; but do when she isn't. Setting out decoy reagents and the reactions work. Unless you set up CCTV cameras in the lab, you aren't going to get evidence that is much better than this.
My advice would be to talk to the advisor with your fellow group members. Bring along a written summary of the evidence and concerns. Leave out the aspects of Sarah's personality (micromanager, ridiculing others, etc) and stick to the "sabotage facts". Keep calm: your PI might respond with shock or anger (if they have suspected nothing up until this point), you don't want to derail the discussion. 
If your PI refuses to admit there's a problem or does nothing, then you might consider talking to a university ombudsman (impartial mediator) to get advice on what to do next. Or resigning from the lab if you don't want to support unethical research. Hopefully the PI will listen to your concerns. 
In the interim, try to keep your research secured and confidential. That might mean locking up your lab notebooks, setting up decoy reagents/hiding your own reagents. 
Sabotaging other people's work is an awful thing to do - but it isn't as bad for the PI w. respect to their tenure/funding/publications as if this student was faking positive data (that subsequently got into their grants or papers). I don't think that concern for the PI's wellbeing should stop you from reporting the suspicious behaviour. 

Also, don't talk yourself out of things before you even try!
Apply for the REUs anyway. Apply with self-confidence. I'm a foreigner doing a PhD in the USA - although I'm ineligible for a lot of funds and awards, it just means I need to search harder for those I can apply for. Volunteer to conduct research during the semester. 
The great thing about grad school is that the coursework (and testing) is basically done with. Your ability to conduct research is a more important trait in grad school than your ability to score highly on tests. You don't need a perfect GPA: as others have said, focus on the positive exit trajectory. 

I agree with how you're thinking about this, and think that PI A sounds like a good choice. 
You shouldn't be working on a research project that bores you to tears...but nor should you sacrifice your own happiness and professional development/training just to do that one research project. There's always the risk that your dream project will fall through: PI doesn't want you to work on that; project fails completely and you need to work on something totally different; you realise you weren't as interested in the topic as you thought you'd be. 

I agree with how you're thinking about this, and think that PI A sounds like a good choice. 
You shouldn't be working on a research project that bores you to tears...but nor should you sacrifice your own happiness and professional development/training just to do that one research project. There's always the risk that your dream project will fall through: PI doesn't want you to work on that; project fails completely and you need to work on something totally different; you realise you weren't as interested in the topic as you thought you'd be. 

What I like to do is send letters to my grandparents. If your grandparents are more electronically-savvy than mine you can maybe do Skype chats. Regardless, although regular contact doesn't match seeing somebody in person...it is still maintaining a strong connection.
It sounds like mentally you are still living at home. You may need to try harder to live in the place your body is (in this case, grad school). That means making a decent effort to find new friends. Sure they may not "get you" in a way your childhood friends do...but that doesn't mean you can't enjoy their company or form a meaningful connection to them. Part of being "got" involves helping people understand who you are by opening up and being honest, and by making an effort to understand the other person. 
What I liked the most about moving away from home into places where I knew no one was that I had to opportunity to try new things without any obligation to others. For example, when I was living at home I did a lot of long-distance running with a group of people. When I moved an hour down the road to university I continued with the running because I was still connected to that social group. However, moving to a new country meant that I could break that pattern and take up new sports. I kinda found it more fulfilling to form a totally new identity in the foreign country, rather than attempt to continue with my old habits. It helped me make a more meaningful connection to this new location and made the experience feel less transient. If there aren't grad student societies you can join in your school, look on Meetup.com for interest/social groups you can check out.
I know that your family wants you to be happy and productive, wherever you are in the world. Your experience in this new location is whatever you make it!

What I like to do is send letters to my grandparents. If your grandparents are more electronically-savvy than mine you can maybe do Skype chats. Regardless, although regular contact doesn't match seeing somebody in person...it is still maintaining a strong connection.
It sounds like mentally you are still living at home. You may need to try harder to live in the place your body is (in this case, grad school). That means making a decent effort to find new friends. Sure they may not "get you" in a way your childhood friends do...but that doesn't mean you can't enjoy their company or form a meaningful connection to them. Part of being "got" involves helping people understand who you are by opening up and being honest, and by making an effort to understand the other person. 
What I liked the most about moving away from home into places where I knew no one was that I had to opportunity to try new things without any obligation to others. For example, when I was living at home I did a lot of long-distance running with a group of people. When I moved an hour down the road to university I continued with the running because I was still connected to that social group. However, moving to a new country meant that I could break that pattern and take up new sports. I kinda found it more fulfilling to form a totally new identity in the foreign country, rather than attempt to continue with my old habits. It helped me make a more meaningful connection to this new location and made the experience feel less transient. If there aren't grad student societies you can join in your school, look on Meetup.com for interest/social groups you can check out.
I know that your family wants you to be happy and productive, wherever you are in the world. Your experience in this new location is whatever you make it!

What I like to do is send letters to my grandparents. If your grandparents are more electronically-savvy than mine you can maybe do Skype chats. Regardless, although regular contact doesn't match seeing somebody in person...it is still maintaining a strong connection.
It sounds like mentally you are still living at home. You may need to try harder to live in the place your body is (in this case, grad school). That means making a decent effort to find new friends. Sure they may not "get you" in a way your childhood friends do...but that doesn't mean you can't enjoy their company or form a meaningful connection to them. Part of being "got" involves helping people understand who you are by opening up and being honest, and by making an effort to understand the other person. 
What I liked the most about moving away from home into places where I knew no one was that I had to opportunity to try new things without any obligation to others. For example, when I was living at home I did a lot of long-distance running with a group of people. When I moved an hour down the road to university I continued with the running because I was still connected to that social group. However, moving to a new country meant that I could break that pattern and take up new sports. I kinda found it more fulfilling to form a totally new identity in the foreign country, rather than attempt to continue with my old habits. It helped me make a more meaningful connection to this new location and made the experience feel less transient. If there aren't grad student societies you can join in your school, look on Meetup.com for interest/social groups you can check out.
I know that your family wants you to be happy and productive, wherever you are in the world. Your experience in this new location is whatever you make it!

What I like to do is send letters to my grandparents. If your grandparents are more electronically-savvy than mine you can maybe do Skype chats. Regardless, although regular contact doesn't match seeing somebody in person...it is still maintaining a strong connection.
It sounds like mentally you are still living at home. You may need to try harder to live in the place your body is (in this case, grad school). That means making a decent effort to find new friends. Sure they may not "get you" in a way your childhood friends do...but that doesn't mean you can't enjoy their company or form a meaningful connection to them. Part of being "got" involves helping people understand who you are by opening up and being honest, and by making an effort to understand the other person. 
What I liked the most about moving away from home into places where I knew no one was that I had to opportunity to try new things without any obligation to others. For example, when I was living at home I did a lot of long-distance running with a group of people. When I moved an hour down the road to university I continued with the running because I was still connected to that social group. However, moving to a new country meant that I could break that pattern and take up new sports. I kinda found it more fulfilling to form a totally new identity in the foreign country, rather than attempt to continue with my old habits. It helped me make a more meaningful connection to this new location and made the experience feel less transient. If there aren't grad student societies you can join in your school, look on Meetup.com for interest/social groups you can check out.
I know that your family wants you to be happy and productive, wherever you are in the world. Your experience in this new location is whatever you make it!

American chicks will like you and your accent. 
If you are so inclined towards that sort of thing, of course.

Make use of your committee members. Even though your thesis topic is a niche one, don't underestimate the ability of your committee members to (i) understand it (ii) be able to make useful critiques of it. At the very least, they should be able to tell you if your argument(s) make sense to a non-niche-specialist. 
In most fields there is the opportunity to carry out edits (sometimes substantial ones) as an outcome of the thesis defence. The draft you hand to your committee isn't always your FINAL draft.  Don't let a lack of feedback from your advisor make you miss the submission deadline. 

How about searching for a language exchange program at your new university/town? You meet with a person who wants to learn your language in exchange for helping you with English (often done over a coffee or lunch). That could be a nice way to build up your confidence and learn some interesting American phrases. 
My suspicion is that your accent isn't as big a problem as you think - worrying about how you speak makes the problem(s) seem bigger. If you were in an environment where everybody was speaking English as a second language, of course that makes things harder on everybody involved and doesn't necessarily have anything to do with how you were speaking.
On a lighter note - I'm a native speaker of British English...and I can be incomprehensible to native speakers of American English. Not just the words I use are all wrong, but how I pronounce common words. Even within one country you get notorious regional accents that people outside the region struggle with. Nobody has the monopoly on perfect English speech & understanding!

With any kind of stress levels it is important to (i) do stuff other than your research & teaching (ii) take care of yourself. Even when you have a lot of stress and limited time it still means taking some time off at the weekends to do other things; eating well; going to the gym (even a 30 min workout in the morning is great for me); perhaps going home to do grading instead of staying in the lab late.
If the one postdoc is part of the problem, maybe you can try and switch to work with someone else? High standards by themselves aren't a bad thing (more on that in a second): but if the postdoc can't give you useful feedback to learn & improve, or is rude towards you...ask to work with someone else. Obviously you need to be careful how you go about this - and be prepared for mediation rather than a transfer - but it seems like the obvious thing to try first. 
I think it's important to differentiate between "high" and "impossible" standards. PIs want to publish high-quality papers. A quick way to bring a paper's quality down is through things like messy spectra, badly-designed experiments that don't account for certain variables, etc. In that sense, having high standards about how clean your materials are and how carefully you gather data are really important. And it's something that you need to start taking on board as soon as you arrive. But there also should be some logic as to WHY particular standards are expected. And other group members should be communicating the standards before you collect the data and find you need to re-run it all again. Also, the goalposts shouldn't be continually shifting.
The PhD is all about training you to become a better scientist. But not at the expense of making you miserable and destroying your self-esteem. There's no shame in walking away from a situation that's damaging you. 

It sounds like what you need to do most is grow up. You are acting like a child, and it's not surprising that your parents still feel like they can treat you as one. 
This is your life, not theirs. You are financially independent of your parents, so you don't need to do everything they say. That said, I don't think there is any point in deliberately doing things just out of spite. It doesn't sound like you are in a place in your life where you should be making life-altering decisions that you can't take back, including both cutting off your parents and leaving your studies without a clear plan of what happens next. Life changes that really work are done slowly and incrementally, and with a plan. That is what I think you should aim for.
I think the first order of business is for you to start developing some kind of life beyond just what your parents want you to have. What are your hobbies and interests? I am sure that there are things that you can do and clubs on campus that won't require you to spend money; that could be a good way of starting to create a life for yourself. Your time and is yours to choose what to do with. It sounds like you've been devoting 100% of your time to your studies, but that's a choice. You can choose to spend some of that time on yourself, in a variety of ways, including making time for your hobbies, making new friends, joining meetup groups, sleeping, or whatever else works for you. This doesn't mean you need to fully stop your studies, but it does mean that you might want to slow down a bit. Being able to combine work and life, and prioritizing what matters for you, is another aspect of being an adult. A prerequisite to that that I think you might need to work on is finding out what you really want, and that is step one for you. 
At the same time as developing a personal life, making friends, starting to date, etc., you should also think about your professional life. Suppose you don't complete your PhD -- a fully valid decision -- what happens next? You might know what you don't want to do, but do you know what you would replace that with? What are your career goals? What do you want to do once you graduate, and are you right now studying for a degree that will get you there? Find out what resources exist on your campus and take advantage of them. Career centers can be very useful and they are often underutilized by graduate students. Are you taking the right courses and developing the right skills for what you want to do? Should you be taking something else, getting internships, etc? This is another thing that you should have a clear idea of before you make any decisions about dropping out or leaving with a Masters. You can stop at any time, but coming back will be difficult once you leave, so you want to make sure you're making a decision that's really right for you, and that you're making it for the right reasons and not out of anger or out of spite for your parents. 
I understand the sentiment that people at the wellness center are useless, but I really think you need to talk to someone. Wanting to hit a stranger for your perceived opinion of who they are and hating your parents and thinking about taking drastic measures in how you interact with them are both things that you'd benefit from talking to someone about. Not to mention actually starting to discover who you are and what you want to do with your life. Doing that can be a difficult process and requires a certain amount of compatibility between personalities, so even if you spoke to someone who wasn't a good fit (and certainly if you just have this opinion without ever having tried to talk to anyone!), it's worth trying again.   

I'm with @Eigen. I think it's important to have some degree of satisfaction with what you do, and it's good to start out with a reasonable level of interest in your research project (but I think at some point in the development and writing of every large project, there will come a time when you hate it all, no matter how much you liked it initially). However, I think that this fantasy that you should only work on what you "love" or only what you are passionate about is a good way to set yourself up for disappointment. In every job you end up doing some things you like less, and research is no exception. I am not advocating for doing something you hate, but I am saying you need to have perspective. There are other factors that matter just as much as the topic, including your fit with your advisor, funding, where there is data, where there is interest in your field more broadly and what jobs are out there, and to some extent, luck. I've said more than once that I'd choose working with an advisor with a better fit but a less interesting topic over the other arrangement any time. This also holds now that I've graduated for picking topics that allow me to talk to those people who I enjoy having around me the most, even if it's a topic that I might not otherwise ever choose. 
You don't have to have your dream project right now -- certainly not for a Masters and I would argue also not necessarily for your PhD. I view my work in a much more pragmatic way; I have a broad set of interests, and what I pursue at a given time is influenced in large part by the people around me who I talk to and what their interests are, where the money is and what gets funded these days, what gets accepted at conferences, what job ads say they want (and who actually gets hired at the end of the day, a somewhat different metric), and what I actually have time and access to data for. I wouldn't do things I absolutely hate (for very long, if I can help it), but there are definitely things on my wish-list that I am not getting to right now because I think the time just isn't right. 

Personally, I'm of the opinion that graduate school is about learning skills and developing abilities, rather than getting to pursue the research you've always dreamed of. 
I've had too many peers not end up with degrees, or end up taking years longer getting to the stage where they are independent researchers because they kept only wanting to work on projects that they "loved". 
Especially for a MS, where you'll only be there a couple of years, I'd buckle down, find a lab with funding, and graduate. You aren't tied to what you do as a grad student for the rest of your career, and getting a degree and moving on is the important part.

From the phrasing of your post, I wasn't sure if you actually had started the program, or if you're going to start in the Fall. 
If you've not yet moved to the new location and started off, then I'd recommend giving it a semester at this new place. Location and happiness in said location definitely matters. But it's also hard to properly judge a place until you've spent time there. For example, as a Savvy Urbanite you might think that Small College Town would be a nightmare to live in...but in fact you find out that its relaxing, rather than boring. As a fellow STEM person, if you find a good PI/lab set-up then I'd urge you to hold on to that (those things aren't easily replaceable!). Your cohort matters too: it isn't always easy to make friends when you're in grad school, if you are part of a friendly cohort then you have a social circle/support network already in place. It is valid to transfer for non-professional reasons...but there are a lot of factors to consider when making the decision.
From what I've seen, "transferring" as a first year is the most common thing. However, people usually "transfer" to schools that had made them an offer in the last application cycle (the other school had evidently liked the look of you, so they are usually willing to take you as a new grad student usually without a re-application). But yes, you start over as a 1st year in a new program. 

Hey! I've done A LOT of long distance travel and have gotten pretty adept at conquering jet lag. Some of my tactics are a little late for you this trip, but I'll outline them anyway.
1. Before you travel, try to shift your regular schedule an hour or two in the direction you will be going. This effectively reduces the time difference. So if I (in the UK) am going to the east coast of the US, I might wake up an hour later than normal, eat lunch an hour later, go to bed an hour later. Obviously if your work isn't flexible this is less easy and not necessary but it does help.
2. Get a good nights sleep before flying. Ensure you're very hydrated. Eat healthy food (yes junk food is tempting but it makes your body feel like crap which is exacerbated when traveling). Move around on the plane. Avoid alcohol if possible.
3. As soon as you get on the plane, change your watch to the time zone you are headed to, then try to do everything to that time zone. This may be out of sync with the rest of the cabin but again, it's trying to familiarise your body with your new time zone.
4. Depending on when you arrive, eat a meal at the local time zone appropriate time. Go to bed at a normal time for that time zone. You'll feel groggy and non-responsive, maybe a bit hungover if you've landed early that day but push through. When you go to bed you should be exhausted. If you've jumped forward in time and it's meant to be bedtime but you're still very much awake, go through the routine of bed time. Have a shower/hot bath, brush your teeth, do your moisturizing/facial routine, tuck yourself up in bed with a book (avoid screens). If you find you're still not sleepy, try some meditation and if all else fails there are some excelllent youtube videos on meditating yourself to sleep (it's practically hypnosis). I find these very effective.
5. Set your alarm to wake you up at a reasonable time the following morning. Regardless of how you feel, get up, eat breakfast, do some light exercise (go for a walk, a swim, do  some stretching, something to get the blood flowing) and set good intentions for the day. Remember to still drink lots of water - you'll be dehydrated from flying for a day or two afterwards.
There is no easy fix for jetlag but these tips do help minimise its effects. 

Progress in a PhD program comes in waves, rather than as a steady torrent. I've had some months where I've cranked a lot out of data and made progress towards publishable data (journal publications are the currency of PhD progress in my sub-field). There have also been stretches where I flagged. Or where I ran a lot of experiments but had only negative results to show for it. 
The point is: you have 5 or so years in the PhD program. One slow year doesn't signify doom! You have one productive year under your belt...so that means you're capable of being productive when balancing stuff like teaching and applying for grants. 
Part of the challenge is to manage (self)-expectations and keep your internal/external voices calibrated. What might be "useless research" and "no progress" inside your head could well be "cutting edge research" and "good progress" to onlookers. There are some advisors who will always be under-satisfied with research progress (I don't know if your advisor fits into this category, but there are plenty who do). The fact he's giving advice about the Masters' thesis is a good sign he thinks you can improve your research output (if you were a lost cause, why would he bother helping you?!).
I know that the classes will be a challenge, but enlist as much help as you can. Consider hiring a tutor or bribing a calc wiz you know with lunches/coffees for their assistance. Make eager use of the office hours. Ask your colleagues to see if anybody can lend you their old notes/textbooks/practice problems/past exams. 
Bottom line. Dropping out is an over-reaction. Keep swimming!

For the emotional component of your experience, I strongly recommend that you focus on your sessions with your therapist, especially in regards to coping with the way you feel.
From an intellectual standpoint, I recommend that you try to think differently about your experiences as a graduate student. You passed your qualifying exams, full stop. If the exams revealed areas where you would benefit from improvement, then put those areas on a "to do list." Don't beat yourself up. If anything, you might celebrate the fact that you passed qualifying exams without the background that students in your area typically have.
Second, you didn't win a NSF, you EARNED one through the hard work you've done so far and for the potential for future achievements that you've demonstrated. Draw confidence from what you have done. 
Third, recognize that graduate school is often a "self taught" affair. Advisers don't always offer the kind of support one would like. (I am NOT bitter about this dynamic. Not at all.) One of the things that you can teach yourself is the skill of finding other people who are willing to help you and resources upon which you can rely.
Fourth, understand that your research is not useless. Based upon your comments, you're on the leading edge. It may well be that the pain your feeling is partly due to the fact that the leading edge is often the bleeding edge. Give some thought to finding ways to connect your work to existing trajectories of research. Use that research to strengthen your foundation and your work may feel more "connected." Also understand that by being on the leading edge, that by getting there first, you will be defining subsequent scholarly debate. "Geographyrocks? Heck, that person got it right/got it wrong and I'm going to spend the next five years proving it!" 
Circling back to the emotional component, focus upon the usable guidance you developed while working with your therapist.
 

Wear cycling shorts and change once you get there?

If the person is in denial about their alcoholism, how do you convince them that they have a problem which needs to be fixed? At the risk of flippancy, it sounds like from Maelia's description that the person has already made full use of their agency to decide that they don't have a problem and continue with their current behaviour. 
Does it matter if a person is creating a hostile work environment because they have an untreated medical condition, or because they are a (healthy) asshole? From an HR standpoint I'm not convinced that it does - simply because there's an explanation behind every act of harassment, discrimination or micro aggression in the workplace, and I don't think it is the place of the employer to decide that a particular act of harassment can be mitigated/weighted differently based on individual circumstances. Nor are employers obliged to fix underlying problems. They can point you in the direction of counselling, cover addiction treatment under their insurance program, etc...but it's up to you to make use of that. 
I agree that banning this individual from public events isn't a nice option...but maybe it would be a wake-up call to this person that their behaviour is a problem? Though, that said: this person is an alcoholic, are they getting drunk at other times (i.e. not just at Dept-sponsored seminars)? If they're going to use the absence of alcohol at seminars to get drunk(er) at lunchtime instead, has the problem really been dealt with?
 

In our Dept, any coursework queries are handled by the grad program administrators. I would take your concerns & questions to them, rather than involving your advisor. They're the ones who usually know best! They can also give out special permission numbers for our classes. 
Try asking one of your fellow grad students who is in your area of research but a few years ahead. How did they navigate the coursework? 

If you WANT to spend your whole day working in sweaty, smelly clothes...then that's fine, I guess. :S 
The other folk you come in to contact might have differing opinions on this. There are bigger issues at stake here than your scrotum, bruh.

Wear cycling shorts and change once you get there?

It won't be that easy to move to a new school. They will have to arrange a visa for you, which can be both expensive and time consuming. I think you may have no choice but to leave. More generally, though, I don't think it'll matter if you have a summer RAship somewhere in the US when it comes to applying to a new MA/PhD program. As I said in a different thread, the important question is going to be whether you'll be able to get anyone from your current school to support a reapplication (= write you a strong LOR). Without one, there will be a big red flag in your application. I would interpret the "false hopes" you have been getting as soft rejections which you haven't been understanding correctly. And I would give some serious thought to what that means for what your department thinks of you and how they'll react if you ask them to write you a LOR. I think you should work hard to leave on good terms and mend fences to the best of your ability, to give yourself some chance of coming back to another program in the future.