OP- anyone can apply for financial aid. What we are trying to tell you is that you are not going to get enough to afford NYU.
You do not qualify for various funding programs that are available for US citizens (Federal loans and grants). You cannot commute from home to cut down on costs. And in order to get a visa you need to demonstrate that you have every nickel you will need for all four years.
You bring up the currency fluctuation which is an excellent point. There are no guarantees that next year, the tuition won’t be even higher due the strength of the dollar. Then what?
Find a cheaper option. You cannot afford NYU and your parents don’t understand how the US educational system operates if they continue to encourage you to just apply for a couple of scholarships to make NYU work.