US Applicant Needs Help - When do you get offers? Too many/too little AP Exams?

First and foremost, speak to some British students too, because they are your main competition depending on the ratio of a universities foreign students. I'm British so won't be able to answer all your precise questions regarding the US/UK application differences and I unfortunately do not know how many AP subjects is the average for US international students applying in the UK, but I think this might help anyways (but do see if you can find some of this info out so you give yourself a fighting chance). Go through TSR and ask many, many questions. Annoy people.
1) When did other US applicants hear back from unis?(Would really appreciate experiences from anyone but I'm especially curious about UCL, LSE, KCL, SOAS, Loughborough, Manchester, Warwick, Durham, or Bristol)
I can't say I know when universities give international students their feedback, but I found out from KCL in my application in November, and then UCL and LSE in June (which sucked). But, I have heard that universities prioritise international students results first, so go find a forum and ask away. Let me know if you need any feedback about the unis themselves as I've been to most of them/have friends going so I might be able to help.
2) Is there a thing as being too qualified/having too many AP exams hence being rejected as unis might think you're applying somewhere else? For examples, some schools only require 2 or 3 AP Exams but I have 6. Would that put me at a disadvantage?
I cannot in any world imagine that too many AP subjects would result in you being penalised. The very important thing for consideration is that the US/UK education system and thus applications for higher education are massively different. If it's easier, think about AP subjects as being comparable to A-Levels (the qualification most British students apply to uni for, taken at 16-18). This may be why some schools require 2-3 and other's might differ. The very important think for you to know is that every university is very different and do thing's very differently, despite UCAS acting as an apparent middle-man. Go ask forums, visit the unis if you can, watch lectures, email the universities etc etc. Universities want international students, so get in contact with them and do some digging, you'll find the answers you need somewhere.
To continue on my point of our education systems being different, don't do the whole extracurricular thing. The reason you may be penalised for having 6 AP subjects is that if you say that, then don't expand. You need to back up your interest in the course you're applying for, plus the subjects you've done in the past, by showing you've done extra work in the area you're interested (in your case, politics and international relations). Put it like this, sure, you can weasel in a mention of your music talents, or dedication to soccer and hockey, but if you waffle about it, the person reading your application will skim it and find it much less compelling than someone that has proved they're interested in the uni course. Sorry to rant, but this is super important to understand. Extracurriculars can be anything - that one debate event you went to at 13 that introduced you to political speaking, the essay competition you wrote that meant you researched extensively about a politician/a scandal/a historical event/anything remotely political related. It can be a book, a podcast, a magazine, just something with information you took away, developed, showed an understanding of, and built off.
3) Since everyone applying to top unis such as Oxford, UCL, LSE, KCL all met/exceeded the minimum requirements, how do these schools differentiate between US applicants? I only have 6 AP Exams compared to many US applicants who hold 10+ AP Exams because my school doesn't follow the AP system and students have to self-study for AP exams. Would you say it's about who has the most AP exam results who gain admission into these top schools? Or if you meet the minimum requirement, would admissions simply evaluate you based on your personal statement and extra-curriculars?
Okay so again, in the UK there are straight A* students at A-level, have done competitions in the subject they want to study, have read many books, watched tons of documentaries, done every extracurricular, had every tutor - and still not got into Oxbridge/London unis. In fact I know several. Not to be cringe, but they want to know who 'you' are. Oxbridge for example, will pick the student in the interview that asks a question, or asks the tutors to define something they say, over the student that knows precisely what they mean and gives a formed opinion. They want thinking, and they want development. If you're perfect already, what work do they need to do? That's always important to consider. Plus, remember, all universities look for different things in their students purely off of the course, people who have been before, the tutors/admissions etc etc etc. You can't really control those factors.
What you're really asking is what would define you as a good student over others that are equally as high achieving. And the answer is simple. It's not who has the most AP subjects because British education is very much quality>quantity as we specialise in school early with GCSE's and A-Levels. Everyone can get a good grade if they try hard enough, not everyone can write a PS that conveys genuine interest in their course, that has obviously researched said course and knows what the uni is looking for, that conveys who they are as a person, includes really interesting supercurriculars and probably mentions some extracurriculars too. That's what you need to nail. As you said, if you hit the minimum (though it's not really that, it's more general entrance rate) they're look at the statement first and within that your supercurriculars. I don't really know if there's a section or something given to the US students for extracurriculars for consideration, so you'll have to ask. I wouldn't imagine there is but you never know as they're quite important in the states and only worth a small mention in the UK PS if necessary. If you have a doubt about your number of AP subjects, slot it into the personal statement that you self study because it shows drive and dedication. Let me know if you need more advise regarding the personal statement itself, I could write for hours.
4. LSE requires applicants to submit a GPA. What should I do if my school doesn't have GPAs? And if I did have a GPA, how would LSE even see it as there isn't a space on UCAS to submit transcripts?
Put it in your personal statement easy peasy. Universities are remarkably flexible, but LSE/UCL can be uptight so email the former to get proper advise from the uni regarding the GPA issue. You should be able to enter your current grades on UCAS. The UK doesn't really do 'transcripts', so when I had to submit mine to a US school they just took my raw A-Level grades. Again, I'm not sure exactly how grading AP subjects goes in the US, but there should be a way to figure it out and put it onto UCAS. British students have to do their GCSE's (done 14-16) each and it's painstaking so good luck!
I hope that's helped a little! Ask me any questions and go ask around several TSR forums. I'd probably recommend looking into the unis you're most interested in/have the best courses and ask their forums for international students advice (though your best bet is asking on Oxbride and London uni forums because they have quite a few international students). Email the schools or call them up, and go through as much of their website/information you can handle without your brain going kaput. I believe in you!

I would just pick out two points from the above - firstly for LSE GPA I would not put this in your personal statement, you should be able to add your HS diploma with subjects and GPA in the qualifications section. And if not this would be for your academic referee to note on their reference (as just writing in your PS tells them nothing - anyone can write any number in that!).
Secondly for applying to Oxbridge as noted above it's not simply a zero sum game about grades. The interview is the key part because what they want to see from the interview, is how "teachable" you are in the specific, unique teaching format at those two universities namely the tutorials/supervisions (confusingly plenty of other unis have timetabled actvities called "tutorials" but these are not the same as an Oxbridge tutorial). Tutorials/supervisions at Oxbridge are normally I gather between 1-3 students and an academic (which may be a PhD student sometimes) where you will go through a piece of work prepared specifically for it (typically an essay for essay based subjects, for others it might be e.g. problem sheets or similar).
From what I gather generally the point of the interview is they want to give you a question you don't know the answer to and see how you reason using what you do know to an answer for it, and want to see how you explain your thought process in arriving at the answer. My understanding is they may give you prompts if going down the wrong route, or they may then ask you to reconsider some part of the premise of the question to see how you respond to that new information and explain in view of it.
So there may well be students who are excellent students, get top grades in everything, but simply aren't suited to that kind of intensive 1 on 1 (or 1 on 2/3) teaching format - that's not to say they aren't very intelligent individuals, just that they may benefit from a different style of teaching and learning (e.g. more traditional lecture formats - which they also have at Oxbridge but the tutorials are pretty central to their teaching I gather). So they may identify those students through interview and choose not to make an offer to them.

Hello! I'm a US applicant applying for History and International Relations/Politics (depending on the school). I have all 5s on 6 AP exams. I would be super grateful if anyone is able to answer my questions!
1) When did other US applicants hear back from unis?
(Would really appreciate experiences from anyone but I'm especially curious about UCL, LSE, KCL, SOAS, Loughborough, Manchester, Warwick, Durham, or Bristol)
2) Is there a thing as being too qualified/having too many AP exams hence being rejected as unis might think you're applying somewhere else? For examples, some schools only require 2 or 3 AP Exams but I have 6. Would that put me at a disadvantage?
3) Since everyone applying to top unis such as Oxford, UCL, LSE, KCL all met/exceeded the minimum requirements, how do these schools differentiate between US applicants? I only have 6 AP Exams compared to many US applicants who hold 10+ AP Exams because my school doesn't follow the AP system and students have to self-study for AP exams. Would you say it's about who has the most AP exam results who gain admission into these top schools? Or if you meet the minimum requirement, would admissions simply evaluate you based on your personal statement and extra-curriculars?
4. LSE requires applicants to submit a GPA. What should I do if my school doesn't have GPAs? And if I did have a GPA, how would LSE even see it as there isn't a space on UCAS to submit transcripts?
Thank you so much for your help!

Hello! I'm a US applicant applying for History and International Relations/Politics (depending on the school). I have all 5s on 6 AP exams. I would be super grateful if anyone is able to answer my questions!
1) When did other US applicants hear back from unis?
(Would really appreciate experiences from anyone but I'm especially curious about UCL, LSE, KCL, SOAS, Loughborough, Manchester, Warwick, Durham, or Bristol)
2) Is there a thing as being too qualified/having too many AP exams hence being rejected as unis might think you're applying somewhere else? For examples, some schools only require 2 or 3 AP Exams but I have 6. Would that put me at a disadvantage?
3) Since everyone applying to top unis such as Oxford, UCL, LSE, KCL all met/exceeded the minimum requirements, how do these schools differentiate between US applicants? I only have 6 AP Exams compared to many US applicants who hold 10+ AP Exams because my school doesn't follow the AP system and students have to self-study for AP exams. Would you say it's about who has the most AP exam results who gain admission into these top schools? Or if you meet the minimum requirement, would admissions simply evaluate you based on your personal statement and extra-curriculars?
4. LSE requires applicants to submit a GPA. What should I do if my school doesn't have GPAs? And if I did have a GPA, how would LSE even see it as there isn't a space on UCAS to submit transcripts?
Thank you so much for your help!