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First of all: Looong text. I am sorry, but I will not write that much.
No matter how good you are, IVY's are always hard to get in.
Either you have a connection to alumni, or it will stay that way.
IVY's are not universities of the best education. They are among them.
Mainly, they are prestigious. Therefore a lot of students apply to them.
Therefore, getting accepted is always hard.
As long as your grades are not severely under their target group, this is my opinion:
Your choices are reasonable.
Apply to as many colleges as you are willing to pay the application fees and to write essays.
Just be okay with getting rejected. There is no reason to be afraid.
I will not give you any suggestions for schools because it is a personal choice of preference what schools one wants to attend.
You can make use of CollegeVine's approximated chances if you are unsure.
Not bad. But there is no guarantee. I have seen "more impressive" applicants that have gotten rejected, but I would say that the biggest factor that is severely underrated is LETTERS OF RECOMMENDATIONS. These are a hit or miss. If you can get an amazing letter of recommendation, Ivy Leagues will become way easier.
I don't think I'm qualified to answer all your questions but you seem like a very strong college candidate within the United States. Elite colleges are looking for someone who will most likely graduate from their college to go out into this world to make a difference. Being well rounded helps, but showing strength in a particular subject or intended major shows the most passion and dedication. Having national or international rankings in anything looks really impressive (which you mentioned you have in olympiads). If you can dedicate yourself to having strong essays, getting the best possible grades, and doing what your currently doing, you have absolutely nothing to stress over so don't worry about it too much.
First of all, don't be afraid of applying to top schools. The worst that can happen is that you get rejected and that's that, but you never know if you'll get in until you try. As long as you can pay for the application (or get a fee waiver which might apply to you), I would apply.
In terms of EC's, you seem to have plenty of achievements. Choose which ones you want to put in your application by where you have the highest achievements, and which ones fit best into the major you want to go into/the picture you want to paint of yourself to the AO. Though you can't find a focus in all your activities, you have enough to pick and choose to create a spike (one strong point).
To choose colleges, I can't tell you where you should apply specifically, but do your research and know what you want from a college in terms of things like financial aid, offered majors, location, community, etc. I think that colleges that are really good for double majors/interdisciplinary studies would be a good fit for you since your interests seem to be widespread. Also, look at places that are a good fit for any major (well-rounded schools) because you have interests in STEM, business, and the arts, and those are all really different and you should aim for places where you can succeed no matter what you end up deciding you want to do. I can't really give you chances for colleges either but I would look at the chancing calculator here and the stats of the school in terms of things like admissions rate, average SAT/ACT test scores, and average GPA.
When you're putting together your application, just be yourself (because if you don't fit into a college you shouldn't try to make yourself fit, it's just not a good fit), though you can bring out certain parts of your activities and interests if they fit more with a certain college. For example, if a college specializes in STEM, include more of that. Looking at the college's mission statement and researching the college can help you figure out what kinds of students a college is looking for, as well as attending their online panels/visits.
Sorry this is so long but I hope I answered all your questions!
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