St Andrews Lynx

Yep, same. I've also been to quite a few conferences where if you ask the organizers nicely (and especially if you don't have your own funding), they will let you register at the reduced student rate even if you've already graduated. Name tags never indicate status or how much you paid in registration fees, that's entirely unimportant. Worth asking the organizers, OP, even if just as clarification "Dear organizers, I was wondering if postdocs should register as students or faculty" (except, of course, if there is a special "postdoc" category. In my field there almost never is). You never know, they might solve your problem for you.  

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. 
 

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. 
 

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 know this is not what you want to hear, but do not rotate in that lab. Your first two rotations should be in labs that could potentially be your thesis lab. If after your second rotation you know where you will join, then you can use your third rotation for a technique or a topic. Most people use all three to find the right lab or they join as soon as they find a good fit. 
This PI seems really nice. He is being nice by offering a rotation position, but it may not be the most professional move. You should respond by thanking him for the opportunity and the information, then tell him that you want to use your first rotations to find a thesis lab. If he's still there after your second rotation and you know which lab you are going to join, rotate in his lab then. 

I'd like to chip in with some extra advice. 
All sorts of teaching can be educational for TAs. In the worst case scenario, where the professor is actually a messy, unfair, dull cartoon, you can see situations that you would handle differently: the what-not-to-do situations. If this professor is in fact a bad professor (in what ever sense this could be), then you can think of ways in which you would do things differently. Here are a bunch of possible questions you can observe: 
Are they disorganized? (How would you organize your classes?) Are they unfair? How? (How would you handle the issues more fairly?) Are they boring/disengaging? (How would you engage students?) Do they have a bad presence in the class? (low voice, monotone, hiding behind desk, etc)  You can imagine others. 
Also, the bright side of being a bad professor's TA is that you can meet with them periodically, ask questions about the reasons for ways they handle things, and even make suggestions. (Of course, this depends a lot on other factors. I TAed for my advisor so I was a little confident in making suggestions). 

Have you applied or been formally admitted to the program yet? I can't quite tell from your post.
I've you've not applied yet, the PI might be assuming you are going to apply to the Chem PhD program and then carry out biophysics-esque research in their lab. If you're applying/accepted to the Biology PhD program then as others have said you need to check if the faculty has a dual appointment, etc. 
There should be a graduate handbook and course listings online for both the Chem & Biology programs (you can also look on the Chem Dept website to see if your prospective PI is listed as affiliated faculty there). I suspect if your background is in Bio then the course requirements for a Chem degree could be challenging (or an unnecessary time sink), but there are often options to take classes in other departments that could count towards your degree (this is something you'd need to talk about with a graduate advisor/administrator).

I think pre-emptively calling off a relationship before they even start grad school is too extreme (and does sound like "an excuse to leave him"!). I've seen people break up shortly after starting their Chem PhD...but not at a higher rate than after starting other major life events (e.g. breaking up after you start college/your first professional jobs). 
If you want to stay with this guy...stay with him. Maybe you'll break up with him partway through grad school...but maybe you won't (and wouldn't that be better than breaking up with now?). Maybe you'll break up with him after he gets his PhD. Who knows unless you try to make it work?

Start reading the book. During the semester simply read for 10-30 min each night in bed before you go to sleep. You'll get it finished.
 

As others said here, I don't think you are in the right in this case. As a Masters (or even a PhD) student, you don't get to choose your research project and your advisor does not have to take your research ideas into consideration when assigning you work to do. Ultimately, it is your advisor's prerogative to assign you to work on whatever he or she wants you to work on, and it's your choice if you want to work for that advisor or not. Keep in mind that for the majority of students, because funding is tied to whatever projects have grants, I would say that the vast majority of students are working on projects that their advisors chose and designed, not the other way around.
if an advisor led you to believe that you would be working on X and then suddenly changed it to Y without a good reason, then that wouldn't be good behaviour. In your case, I don't see anything that should have caused you to believe that you get to decide your own project ("no objection" is not the same as "approval"). However, that's not necessarily something that is worthy of a complaint.
In addition, there are often lots of good reasons for an advisor to want their student to suddenly switch projects. For example, if a grant proposal didn't get funded, it might mean the advisor needs to pay you out of a different grant and therefore needs you to work on another project. In your case, there is no funding, so other valid reasons for switching may be: 1) priorities in the lab/research group changed due to internal or external pressures, so they need people to work on different things now, or 2) another student is more qualified to work in area X so that might mean some other students get switched to area Y. Just a few examples.
So, based on the details here, I'm just saying that what happened to you is normal and acceptable. I don't see any wrongdoing by the professor and I don't see any reason for you to complain. Of course, what you do is your own decision and you don't have to justify it here (e.g. maybe there are more things that you prefer to keep private). But if you are just checking in to see whether something unethical happened or not (this is a good idea since sometimes bad things happen but students just think it's "normal" so bad things continue to happen), I would say that this is a case where there might have been some miscommunication or misunderstanding, but nothing bad happened.

Okay, I'll voice the possibly less popular opinion. Your responsibility is to yourself. You don't have to stay with him and you are not responsible for getting him better or for educating him. You need to take care of yourself. If you do decide you want to try and stay, I think it's of utmost importance to get support from others. Can you involve his family? friends? do you have a support system around you to take care of you, if you need it? If he wasn't always like this, something must have triggered this, and maybe you can help him through it. Whatever it is, though, you shouldn't do it alone, and you shouldn't let him take it out on you. This sounds like a situation that requires professional help. I know that posting here was probably already hard enough, so maybe the next step is for you to find counseling on your own, maybe through your school, before you think about talking to him. Figure out your resources and support network, then come up with a plan to confront him. I hope that there is no fear of physical violence, but if there is, let me repeat again: your responsibility is to yourself first. Make sure that you are safe, and take care of yourself, both physically and mentally. If that means you need to leave him, I think that's totally understandable and no one from the outside can judge. And if you choose to stay and try and fix it, again I hope that no one will judge and that you can find the help you need. 

The problem is with *them* and *their* insecurities. It has nothing to do with you. Grad school is great at bringing up all a person's self-doubt, fears and weaknesses, in part because it is much less structured than undergrad. To combat their own insecurities, people bitch about others for working too hard. Or not working hard enough. Or wearing pink cardigans all the time. Or whatever. 
 
You say that you have some friends in the cohort? That's great. Focus your energy on them. It is possible that once your cohort move away from the coursework and get more settled in to their own research that they'll calm down a bit and stop with the nastiness. 

Yeah, it was probably not a good idea to talk to your everyone else but your PI about the sabotage. Regardless of the validity of the concerns, pumping it through a rumour mill rather than going through professional channels undermines your case and leads to too many hurt feelings. It sounds like the comments you made about Sarah prompted your friends to behave in ways - as you said - out of your control. And now she has the opportunity to play the victim, not necessarily without justification.
I get the feeling that the sabotage described is only the tip of a whole f**ked-up iceberg of a dysfunctional lab. If the situation is really worse than this anecdote, I'd consider leaving the lab as diplomatically as possible before (i) you are fired (ii) something even worse (professionally or personally) happens. You don't want your future career tarred with what has been going on around you.

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. 

It does feel like an over-reaction. I think you may be both blowing this out of proportion and under- or misestimating the importance of being able to present yourself orally in a variety of occasions. Writing ability is important, but if you can't sell your ideas in person as well, you'll suffer as an academic. If you give an atrocious job talk or you aren't able to answer questions from left field (and some people specialize at asking those at job talks!), you'll have a hard time getting a job. Students might ask you any question out of the blue, whether or not it's actually related to what you are talking about. And similarly at conferences you might be able to prepare for the talk, but it's very hard to prepare for the question period. You can't panic and run off-stage every time someone asks you something you weren't prepared for. (And here, in fact, you've gotten several weeks precisely in order to prepare!) That aside giving engaging talks is a good way of getting yourself and your ideas out there, or getting invited to conferences and to give talks, and the conversations of the kind you have when not on stage are important for building connections. Those are sometimes as important, if not more, than the actual ideas you're trying to sell, and you can't control the direction they go in.* I'm sure you've noticed that success only has some correlation with good ideas. (As in, you can have good ideas and not be as successful, or not as good ideas but really good inter-personal skills, and be quite successful). So, I think this is a more useful skill than you might be giving it credit for. 
That aside, given that there are people around who agree that the current form of the qualifying exam might not be ideal, maybe there is a way to work something out where it's manageable for you but also meets the department's requirements. You'd need to work this out on an individual basis with your committee; I'm sure you're not the first person to deal with serious stage fright. That said, I would advise you not to do or say anything drastic until after you've calmed down, because right now it sounds like you're over-reacting. If you have a supportive advisor and committee, they should be willing to help you through this milestone in your program and move on to the next steps, especially if you're otherwise successful and could have a successful career in your field. Try to figure this out with them before you do anything quite as drastic as taking your grant and walking away. 
 
* For example, I've been asked on some interview what I think were the most important 3 inventions of the 20th century and why. Another person once asked what book I'd take with me to a deserted island. More than once someone asked some version of "young/old man/woman/person I admire in [my field/other field/science]", what paper I read recently that made me change my mind about my research (and what specifically it was), the most impactful paper/presentation of the year, and other things that caught me off guard. Those are just a few example. I doubt the specific answers mattered, but my reaction did. And then of course random people will ask about hobbies, books you've read recently, your favorite foods, recent travels, and any other thing that pops into their heads. Unless you plan to pre-rehearse every possible conversation you might have with other academics, you need to learn to deal with unexpected situations, including high-stakes ones. 

Yeah, it was probably not a good idea to talk to your everyone else but your PI about the sabotage. Regardless of the validity of the concerns, pumping it through a rumour mill rather than going through professional channels undermines your case and leads to too many hurt feelings. It sounds like the comments you made about Sarah prompted your friends to behave in ways - as you said - out of your control. And now she has the opportunity to play the victim, not necessarily without justification.
I get the feeling that the sabotage described is only the tip of a whole f**ked-up iceberg of a dysfunctional lab. If the situation is really worse than this anecdote, I'd consider leaving the lab as diplomatically as possible before (i) you are fired (ii) something even worse (professionally or personally) happens. You don't want your future career tarred with what has been going on around you.

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. 

Anything worth thinking is worth over-thinking.

I got into the new lab!  This lab is even more tailor made for me than the last lab.  If anything I am annoyingly tenacious, so that definitely helped me through the application process. I wanted to post this update because so many people in this thread helped me through one of the darkest times in my career.  Thank you from the bottom of my heart! Also, to those that private messaged me expressing that they were having similar experiences, please trust your gut.  If your gut says "run", run. There will always be other opportunities out there.  If I had stayed in that lab my work would have been subpar and the stress would have taken years off of my life.  Now, I am onto better and brighter things.   

There are some labs where PI will place new grad students on a project that guarantees a quick publication (something that has already been partially-developed by a previous student, etc). Other times you'll work with a senior student in the beginning. This is something to clarify before you join the lab. You'll also need to see what is typical in your new lab - do most people get a publication before the end of their 2nd year, or do most people graduate before they can publish anything? You might have to tone down your goals (or find a new program) if your expectations don't match up to what ~80% current of grads in your program/lab actually achieve. 
The most obvious suggestion if you're stuck with a senior student...work hard and don't complain. Show you can do what is asked of you in a polite, timely manner. Make an effort to deploy your best experimental technique and show that you can work up to "publication standard" (in synthetic chemistry this would mean being able to isolate good yields of clean products and getting pretty NMRs for the paper's SI). Be engaged, mature and show you can handle responsibility. 

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!

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

The earliest you can enter the USA on an F1 visa is 1 month before the official program start date. I came as early as I could - which allowed me to explore the area a bit before it became over-run with students. Maybe 1-2 weeks - give yourself enough time to recover from jetlag, too! 

Announcement: New grading policy! 
[Instructor] has decided to institute a new grading policy. [specifics]. This applies starting with the next assignment. Notice that this means that the numerical grade you will get might change, but the equivalent letter grade will remain the same. Notice additionally that since we are not retro-actively changing the grades on your first assignment, this will lead to some bump in everyone's final grades. 
I have never in my life had a student complain about getting a higher grade than they deserved. 
For any other questions, you refer them to the new grading schema and you point out that the grade corresponds to the same letter grade, and is what they earned on the assignment. I think you're blowing this out of proportion (though again, I don't think changing grading policies mid-semester is ever wise).