You will be informed of your loan awards shortly after receiving your admission decision, but those are federal loans, so they are only for US citizens. I assume that you would have to take out private loans as a non-US citizen.
About a month after the admissions application is due, the financial aid application is due, part of which is an opportunity to write up to 30 (!) essays for various fellowships, most (all?) of which are open to international students. I wrote a few essays, didn't get any fellowships/scholarships, accepted ANYWAY, and THEN was awarded a scholarship.
I think it was based on the subject matter I wrote about in my admissions essay, since the scholarship was quite subject-specific. I assume that both domestic and international students would be considered equally for such scholarships that arise at the last minute. I also have huge financial need, but I do not know if that was a factor in the scholarship decision. I tend to think not. The financial aid office will tell you (and I think it's true), that it is very rare for large scholarships to be awarded after you accept to the program.