I’m sorry your mom isn’t well. That must be tough. How old are your brothers? Will they be able to live with the US relatives you plan to stay with when they’re college age too?
Colleges can ask for whatever they want. Most have a student contribution of some sort. And you’ll probably need to provide proof of acceptable insurance or buy theirs.
What state are the relatives in? If your dad lives there I wonder if you could be considered a state resident because he has residency. If they’re FAFSA only schools, I think only your mom’s financial info. would be required. It would depend on the state though. Some are much harder to get residency in than others.