I’ll address your post as it stands here. Harvard and MIT are need blind even to international applicants , so your need won’t affect your applications there. It could to other schools. You are an over represented nationality being from India, and a lot of schools here do take that into consideration. You need to be at the top of the pool of Indian students applying to the colleges you choose. You will be competing against those seniors from your country applying to the same schools you are. It’s a very competitive group.
I cannot assess your ECs. If they don’t ring some bell for the AOs, not sure how much effort they will make to verify them, check them out. AOs from top schools here tend to have their lists of what awards, honors etc that mean a lot to them.
As a top student, taking the most difficult courses available, and getting great test scores, you would be in the running for a spot at the selective schools. It all depends on who else is applying.
If you really want to to study in the US, and are limited to 10-12 applications, pick 6 selective colleges including MIT and Harvard , and give them a try. Then look for some schools that have good financial aid or big merit awards and find 6 of them as possibilities. Understand that as an international student with need, they will all be reach schools for you. It is possible that some schools where your SAT and academic prowess is way up there, will pay for you to attend there to bring up their numbers.