The difficulty for you is that you know where your dad is. Even though you will be independent for taxes, you will be his dependent for financial aid, and you will need his data for the FAFSA until you are 24. If he truly has no income or other financial means, you will face challenges every year because your FAFSA will probably be flagged for verification.
Have you started classes at Stony Brook? Can you get a meeting with the head of financial aid? Your situation is uncommon. You need to speak with people who can advise you.