Hello. I’m in 11th grade and I want to study math(s) in the US.
My marks are pretty good – I always rank in the top three in the class, although my grades faltered briefly in 9th grade (around an 84%, I have no clue if it’ll kill me). This term, I got a 95%, which is about what I usually score.
I’ve been representing my school, including around five national contests that I’ve won or placed in the top three in, in quizzes (and two national-level spelling bees where I was the runner-up twice) from 3rd grade onward, and have almost ~30 trophies (and over a 100 certs) from these.
I’d definitely require financial aid.
I qualified for INMO (the national-level olympiad, from where some students are invited to the training camp [i.e. the Indian MOP]) last year but didn’t get invited to camp. I could’ve prepared again for this year, but I’ve sort of lost interest in olympiad math after discovering the wonders of “higher” mathematics. I’ve found a mentor (ex- and soon-to-be-again Harvard prof) who now helps me study graduate-level math in my spare time.
- How important is olympiad participation? Is it (near-)impossible for me to get into a good American college (I'm not stuck on, say, MIT, although it would be nice, of course) with these stats? Does the fact that I work on advanced math with a mentor count for anything at all, or should I start working on olympiad math again?
- Is an IMO medal an auto-admit to MIT / Ivies for someone with a profile like mine?
- My mentor was a Harvard prof who left for some time and is again returning to Harvard next year; how useful would a rec letter from him be?
Dang man! If you qualified for INMO I think you have a very good chance for MIT. Honestly in the US, making USAMO (one level less than MOP) is already amazing (but not uncommon) for colleges like MIT. You are sure to stand out. Unfortunately your chances start to decrease as you are an international student and you are requesting financial aid. While the recommendation from your mentor WILL help, I don’t think it will carry too much weight when you are compared with other international applicants. From an American standpoint I would say you have really good extracurriculars and decent grades. Take the SAT (try scoring 2300+) or ACT (35+) and a few Subject SAT exams (1 math and 1 science)(get perfect scores on both). Express your love for higher level math in your essays eloquently and I’d say you would be in the top tier of international applicants (but keep in mind you are competing with other applicants who have scored gold medals in the IMO)
Well, I’ve been told I write well, so I hope the essays should come easy. 
Also, I’d still like to know:
- will the 9th grade marks kill me?
- is a medal some kind of auto-admit for people with similar profiles?
Is there any place I can get a sort of “calendar” for when to get the SATs, subject SATs etc. done? As you can see, I have no knowledge of the “logistics” (is that right?) of the process at all.
Also, I was invited to HCSSiM this year. Is that an advantage?
I wouldn’t call anything an instant auto admit. Why I even know a guy in America who went to the camps for the Physics and Math Olympiads and was a Chemistry Olympiad finalist (along with awesome grades and etc) who was still deferred by the top colleges. Simply a medal will dramatically increase your chances (but once again, if you have nothing else to make you stand out from other international IMO applicants, your chances began to level)
9th marks wont affect you too badly
I worked on some math research with some professors because I was interested in “higher math.” If you do something great related to your interest, it will help you a lot. I wouldn’t say that only a medal will take you to MIT. I have observed that lots of medalists who got into MIT also had something else that was amazing on their app. Try to finish standardised testing before/by september of the year when you will be applying. I don’t think that just getting invited to HCSSiM will help you. If you would have attended HCSSiM, that would have helped you a lot. I have letters of rec from my research mentors, and I’m sure that they will help me a lot. Try making it to the IMO team, it will be a great experience for you. Feel free to message me if you need any help/want to ask questions regarding research in math 
However to answer one thing.
Getting an IMO medal is one of the toughest challenges out there. So if you do get one, it is a testament to your hard work and ability. I hold great respect for the Math medalists because their syllabus is radically different and their thought approach is remarkable.
That being said. One thing is for sure. THERE IS NO WAY IN HELL! That one can get an IMO medal without loving the subject. So when one says that IMO is a sure-ticket to MIT/Ivies, it is because the one holding ticket is that capable. Not because of the ticket is attractive. So just get that misconception out
Also if you love the subject and get it through in your essays, I am sure you will get through.