You have to have a permanent address, and you typically can’t use your dorm address since it’s not a permanent one — I think you usually have to show proof of residency like a lease or utilities bill, so it doesn’t work if you live in a dorm (at least that’s how it is in Missouri; you can read up on Indiana’s policies).
As someone who’s been in the same boat, unfortunately the answer is no. You’ll only be able to get your license in NY, but once you have it you can use it anywhere.
Good luck on your test though! I passed my drivers test (on the second try) two days before I had to go back to college last year, and I go to college across the country. So it is possible!
Yeah it doesn’t matter where its from, as long as its updated. If you were trying to get instate rates for future schooling, then you might want to change your license to that state. But thats only when you become an independent, and you have to change a lot of other forms.