Let each place on your application list know what your current current visa status is (I’m guessing H-1B), that all of your education has been in the US, and that the green card is in process (if it is by time of application). Each place will have its own way of dealing with students in this situation. There are LOTS of them in the US. @paul2752 is one of them.
Ask your guidance counselor to help you find out what the policies are at the public colleges and universities in NY as to in-state status for students in your situation. In some states, you would be considered in-state for tuition and fees at at least some of the publics. @sybbie719 probably knows the rules for New York.
Find out how much money your parents can pay for college, so that you can identify at least one (preferably more) affordable options.
Now answers for your specific questions:
1.) There is no advantage in being an international applicant. The advantage is if you are a full-pay applicant.
2.) Send the art supplement.
3.) As long as you have an affordable place where you know your grades and test scores will get you in, everything else is gravy. Find a true safety (lock for admissions, dead-on affordable), and add in as many pretty safe, match and reach institutions as you feel like.
4.) Try the ACT. A lot of people do better on that than on the SAT.