St Andrews Lynx

Based upon your previous threads about choosing a thesis topic on firstly "Rebutting Ann Coulter" then "Islam & Woman", it sounds like you didn't really know (i) what would make an appropriate thesis topic (ii) how to go about writing a comparative literature thesis (i.e, that it needs to be based off a few pieces of primary literature). You were also changing your mind pretty quickly about what you wanted to write.
 
I can imagine that if your advisor thought you were ill-prepared to write a thesis he might have second thoughts about advising you. 

Snow.
 
F*ckin' snow.
 
Can't they do anything about all the damned snow?!
 
Signed, 
Everybody on the Eastern Seaboard.

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!

Is there another competent undergrad RA that you could buddy up with needy RA? It might help this new RA get out of the habit of relying on the senior grad student "Voice of Authority" for detailed instructions, and instead learn the ropes through a more equal peer-to-peer relationship. TakeruK's strategies are good ones to follow. 
I've seen a lot of undergrads seem to lack confidence when it comes to research - they're reliant on professors telling them exactly what to do at every step. Maybe some you got this one kid! pep talk would encourage them, rather than berating them about their lack of independence. In lab sciences you don't want undergrads doing everything by themselves first in case they spill a hazardous reagent on the floor or break an expensive piece of equipment...but I reckon in the humanities you don't need to worry about that kind of stuff so much.
 

In the sciences (which I'm part of) very few of the professors in my Dept have done any kind of job outside of academia (no years working in industry or teaching, for instance). Their CVs suggest that they took no gap years. What I've seen is a correlation between academics advising their undergrads against taking time off, and having avoided taking any time off themselves. The point for the OP is that their advisors might not be basing their advice on what is best for the OP, but rather what worked well for the advisor. 
The grad students themselves? Sure, plenty of them have real world experience, and have taken several years between their undergrad and PhD. 

Most academics don't have much in the way of "real world experience". I suspect that nearly all of them went straight from undergrad to grad school. If it worked out for them, why shouldn't it work out for literally everybody else? Similarly, since grad school worked out for them, they tend to advise people to go for a PhD because they really don't have any idea of what the other options could be. 
Stupid question. Did you enjoy the research experiences? If you didn't...then I'd advise you against pursuing a research career. Did you enjoy bits of the research experience? Then maybe think about the bits you liked and see what other careers you could follow that would have those things. If there are bits of the research that you didn't like (too much time spent in front of a computer running calculations, group too large, PI too hands-on, etc) then you can formulate a better plan for what you could pursue in grad school and the PI that would be the best fit for you. 
I've seen people go into grad school just because their advisors said "hey, why not consider a PhD", or because it seemed like an inevitable next step. In general it is better to have good motivation and career plans (in which the PhD will help you get where you want). 

If I was in that situation I'd take the free registration, introduce myself confidently as a postdoc and then feign TOTAL IGNORANCE if called out. "Oh, my boss Prof X handled my registration."  (Honestly, given how cheap most academics are they'll probably be impressed with your ability to get something for free)
If it only costs $20 to register as a non-student or something like that then just tell your PI you'll pay for the registration yourself. If it costs something like $200 and the PI would otherwise be paying for your registration...then either swallow the lie or don't go. 
 

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. 

Snow.
 
F*ckin' snow.
 
Can't they do anything about all the damned snow?!
 
Signed, 
Everybody on the Eastern Seaboard.

The thing about academia (and life in general) is that knowing what you are capable of...means bugger all. You aren't admitted to PhD program based upon the strength of you knowing that you can cope with grad school: you are admitted based upon the actual, physical & tangible things that you have produced. Publications, graduate-level written work, grades on a transcript, LORs that judge your actual output. You don't get tenure because you know that you are capable of being a successful research professor - you have to actually be a successful research professor. 
 
My strong suspicion is that if you struggled with the MA, you will struggle also with the PhD. It is easy to correct mistakes - read theses before you start your program, take a break between transitions - but the underlying personal characteristics you possess are harder to change. Mental illness is a chronic thing, if it pops up during your MA it will return for your PhD. The characteristic of under-estimating what you're letting yourself in for will most likely show up in some form or other during the PhD.
 
It is dangerously naive to just assume that your idealised version of yourself will flourish in the PhD program: you need to ask yourself the brutal question of 'Would the version of myself that existed during the MA program, whom my advisor saw...would that version survive a PhD program?" Because although that version of you is the worst-case, nightmare scenario that can't possibly be the real you...that's the version that has a basis in reality. If an outsider read your narrative and examined your physical output, then extrapolated a prediction of future academic success based entirely on those physical/tangible things...what do you think they would predict?
 
I am by nature a deeply cynical person. I do know that people can change themselves - but it takes years, a lot of determination and willingness to accept complete responsibility for your actions. We can hide but we can't fully erase our weaknesses. 
 
Personally I think that your advisors refusal to write you LORs for PhD programs might be the biggest gift they've given you. Don't ruin the next decade of your life attempting to do something that will only damage you.

Snow.
 
F*ckin' snow.
 
Can't they do anything about all the damned snow?!
 
Signed, 
Everybody on the Eastern Seaboard.

Snow.
 
F*ckin' snow.
 
Can't they do anything about all the damned snow?!
 
Signed, 
Everybody on the Eastern Seaboard.

I have sympathy. Sounds like a stereotypical "Assistant Professor in Science". A lot of PIs struggle to learn emotional intelligence when they're on the tenure track if they don't already have an instinct for it; and unless you hit some kind of research jackpot within the next few months the pressure to generate results for papers/grants is only going to continue. Try not to take the PI's behavior personally (it's about their stress, not you as a bad scientist).
As @rising_star says - getting clarity on what you need for a Masters thesis should be your main goal. Accepting that you can't please your PI 100% may also make your life easier.
Is it possible to transfer into another research group in your Dept? Y'know, one where the PI is less...intense? Of course it depends on what your career goals are (you don't need a PhD for everything), but a more established PI might be better for you.
 

I'd phrase it more in terms of feedback on your returned papers ("how could I have strengthened this paper?") rather than the dreaded "If I gave this paper to you now...what grade would you give it?" 
Think about the whole coursework process less about "getting an A", and rather about "writing excellent graduate-level papers". Sure, the outcome of the latter is probably an A, but the grade itself isn't what matters. 

Whatever you do, don't treat this person as your enemy! Academia is a small world: your PI may decide to take 2 students after all, you may end up in the same teams for coursework, or you may put off the PI/lab members by being too mean and thus not get accepted. 
First - come up with a solid back-up plan for alternative rotations. It could be that you don't get on as well in this lab as you thought, or the PI's funding falls through and they end up not taking anyone this year. Treat all rotations seriously and be open-minded.
Second - do the best you can in the rotation. It's not just about putting in the most hours or getting the most experiments done. You want to come across as a conscientious (future) labmate who tidies up after themselves, follows the rules, matches the group personality, etc. A lot of the decision-making for selecting new grad students is based upon personality, values and perceived fit, which is hard to change if you don't match up to what the PI is after and doesn't necessarily mean you're a bad scientist if they don't accept you.

There's a RadioLab episode from 2012 about lucid dreaming - the idea that you can take control of your dreams/nightmares while you're in the middle of them. That may be something to look in to.
http://www.radiolab.org/story/182747-wake-up-dream/
It's great that you've sought professional help and I'm sure that over time you'll see the positive effects increase. 

Whatever you do, don't treat this person as your enemy! Academia is a small world: your PI may decide to take 2 students after all, you may end up in the same teams for coursework, or you may put off the PI/lab members by being too mean and thus not get accepted. 
First - come up with a solid back-up plan for alternative rotations. It could be that you don't get on as well in this lab as you thought, or the PI's funding falls through and they end up not taking anyone this year. Treat all rotations seriously and be open-minded.
Second - do the best you can in the rotation. It's not just about putting in the most hours or getting the most experiments done. You want to come across as a conscientious (future) labmate who tidies up after themselves, follows the rules, matches the group personality, etc. A lot of the decision-making for selecting new grad students is based upon personality, values and perceived fit, which is hard to change if you don't match up to what the PI is after and doesn't necessarily mean you're a bad scientist if they don't accept you.

There's a RadioLab episode from 2012 about lucid dreaming - the idea that you can take control of your dreams/nightmares while you're in the middle of them. That may be something to look in to.
http://www.radiolab.org/story/182747-wake-up-dream/
It's great that you've sought professional help and I'm sure that over time you'll see the positive effects increase. 

Use the internet. Meetup is great for meeting people who share your interests, and the gatherings are already structured (e.g. going out on a hike, having a game night) which makes them easier to navigate. For dating, set up profiles and try OKCupid, Match, etc. You can try looking through the archives of Dan Savage's "Savage Love" - there is advice for everyone everywhere on the dating experience/sexuality spectrum. 
I'd also encourage you not to look at this as a rigid scientific process. If you say to yourself now "I can only obtain a meaningful relationship with a person who has had 0-2 serious relationships"... (i) you limit your dating pool (ii) you stay in incompatible relationships longer because you think this "should" be working (iii) cutesy-newness is overrated. Same with friendship. If you start saying to yourself that only friendships with "mentally-underdeveloped" undergrads could possibly work out...you're going to struggle to find any friends. Some undergrads are fiercely intelligent and will be able to contribute meaningfully to discussions about your research. Some grad students have plenty of friends who are undergrads. Wouldn't it be more useful to have friendships with sociable and emotionally-mature folk, so you could learn somethings from them? Part of having friends in the first place is to enjoy their company: why deliberately seek out "friends" who are awkward to be around?
I think that all good things involve plenty of trial and error to get to. You need to go on lots of dates with a variety of people to figure out who you're attracted to and what is important for you in a relationship. You need to take the initiative when it comes to making friends and be prepared for cool people to blow you off/forget to invite you to their parties. Don't assume that you are too different or inexperienced to form friendships/relationships the way that "normal people" do. Don't expect everything to be perfect the first time you attempt it. 

Repeating the above that you should consult with your school's International Students Office for definite advice.
Some additional notes:
- Your current status is for your PhD program. This means you can only use OPT during the times where your program is not in session or after you complete your degree program (i.e. PhD). Since most PhD programs run year-long, I don't think you can use OPT until you finish your PhD. You also need to be in your current program for at least 1 year to be eligible for pre-completion OPT.
- However, while on a F-1 PhD program, there is something called CPT (Curricular Practical Training) which you could use to take a break from studies in order to do work relevant to your field of study and if it is part of your degree program (e.g. if your program allows you to go on internships, co-op, etc.). Most grad programs don't allow this, but just mentioning it in case. Talk to your international student office about this if you think you might qualify.
- You can change programs though. I think (again, check with experts) if you want to stop at the Masters degree, you should first change your program and your F-1 status to be on a Masters program. Then you can finish your Masters and graduate, allowing you to be eligible for post-degree OPT. This means that you need to reapply and get into a PhD program later, if you want to do that, which will put you on a new F-1 status for PhD program.
I think these are the main ways you can do some OPT before finishing your PhD. Again, talk to your international students office. Hope this info helps you to have some info before going in the meeting though!

You need to talk to your school's International Students Office. You absolutely should not rely on internet sources of any kind when it comes to issues like immigration. That said, my understanding is that you can't work on a student visa, and it's not obvious to me that you can activate your MS-related OPT if you've moved to another program (but you should check that). In case you can, there's some processing time associated with the OPT and you can't start work until that's settled. So it seems to me that if you want a job, you need to be on OPT and do some serious job-hunting; and if you want the PhD, then continue with that plan. Staying in a PhD program until you find a job sounds like it could lead to several kinds of trouble.  -- And again, a disclaimer: I am not an immigration expert. Talk to your school. 

I think that while the undergraduate experience can be thought of as "academic" and "life experience", it's really just "academic/professional" at grad school level. In the sciences, obtaining PhD can be thought of as "your first full-time job". There isn't a lifestyle associated with it to the same extent. 
One big challenge of trying to make undergraduates your main friendship circles (in addition to what has been said on this & another threads) is the question of logistics/schedule alignment. Undergrads typically bond with people who are in their dorms or classes - which is where they do a lot of their "social interacting". The studious ones socialise during hours in the library or in informal study groups. The non-studious ones go to parties. Their schedules are built around classes, internships & work, which means their free time comes at odd intervals. A lot of them will head home on the weekends to stay with their parents. 
As a grad student it isn't easy to fit yourself in to this. You aren't living with them, and you aren't taking the same classes as them. Your schedule isn't going to fit very well over theirs. The socially-inexperienced undergrads are less likely to head out to student groups anyway - they'll spend the evenings in their dorms. The students who get a kick out of meeting new people (i.e. the more socially-adept ones) will be at the student groups interested in talking to new faces. At this point you may as well as try and make friends with fellow graduate students. 
I understand that the idea of tackling "easy" interactions with undergrads is comforting. However, if you want to become an academic you will have to learn how to interact with academics. And I don't think "training" yourself on undergrads alone can adequately prepare you for dealing with 60 year-old distinguished professors or fellow assistant profs. The sooner you can fake being socially-adept (which is what most of us do anyway) with more "advanced" individuals, the easier your academic career will become.  
 

This really depends on what you value more. If you don't want the potential of a bad living situation (due to who you live with) or really need a space that is completely your own, your own place might be the way to go. However, if you feel the need to save a bit more of your stipend and don't want a bad living situation (due to only being able to afford a not great place), go with a roommate. 

If you do go with a roommate, I would do things to try to mitigate issues. If you are someone who needs a clean place, communicate that with your roommate. Open communication and working together can make your living situation a lot better than it (potentially) would be otherwise. 
I know for myself, I have a small loan that I'm paying off and don't want a car (places close to school tend to cost more) so I'll probably need a flatmate. 

You're not good enough to be in graduate school.
No one is good enough to be in graduate school. There is no great platonic abstract of "good enough" which, if obtained, opens the path to tenure with a choir of angels. Everyone's a failure. Everyone is faking it. No one knows what they're doing. Usually, we call this "adulthood". 
Others have given pretty good advice already, and mine is fairly simple: being shit at something is a necessary first step towards being good at something. "Talent" and "natural ability" are bullshit terms that mask the absurd amounts of hard work and/or social conditioning of people assumed to have them. 
Failing isn't an indelible stain on your character. It's a starting point.

If you've been tense for a year and a half and experiencing severe symptoms, you can't expect it all to magically go away in one day or even one week, especially if you're still in the same triggering environment. The best advice I can offer you is to keep doing what you're doing: stick to a routine, and allow yourself some down-time. A holiday, some shopping, that all sounds good. Regular exercise, cooking at home, doing some leisure activity -- whatever works for you -- are other useful things to do. Whenever I accomplish something big I give myself permission to take at least the rest of the day off, more if I can afford it, to do absolutely nothing related to work. It's also nice to celebrate, to have an official recognition of your achievement among friends. I hope you have someone who you can go to happy hour with to mark the occasion. And then, you find something else to focus your energy on. If you're waiting on anything (referee reports? starting a job?) but you can't do anything about it, it's usually helpful to divert the nervous waiting-energy to something else. Work or not, find something to do to keep yourself occupied; that will also help keep you from getting over-emotional. 
And congrats! It was a long road, I'm glad you made it.