First off I'm glad that this thread exists... I can finally find some solace in my fellow international comrades.
1. I applied to 7 schools, got 2 interviews from Vanderbilt Chem Bio and Weill Cornell Pharmacology. Got accepted to Weill so far and still waiting for Vandy. It is indeed soul crushing to receive rejections from schools (and faculties) that you've spent much time reading and researching about. Keep your head up and hopefully by now you've crushed that UConn interview. One is all it takes.
2. My recommendation would be putting more time reading into faculty publications, and tailoring your SOP/PS into why you are a perfect fit with the program you selected. Personal anecdotes of your research experience help immensely. Find someone to polish your essays and school lists.
3. On the topic of selectivity, especially among the Tri-I schools, they are receptive of international students. Both GSK and Weill have dedicated web pages for international students, whereas UCSF has a very blunt message on their admissions pages that says that you should essentially think twice if you're international. In general, NYC is a luminary for an international community considering its history, and I don't think your school choices were unwise at all. You should, however, still call in each school to confirm.
4. My credentials: Taiwanese international. 3.5/4.0 from UCLA, 4/4 UCSF Master's. Two publications. 3 years of research. GRE 161V, 162Q, 5.5W. Make sure to crush the interviews, tell them the school's your first choice, be ready to answer the question "what your research interests are," to which you should list 3 faculties that you'd see yourself working with. In the mean time, get published and get good letters. IMO these two items tell more about an individual's research potential than anything else...