Actually, you do need to be a resident of the domicile where you plan to vote. But all U.S. residents, regardless of where they live, DO have the right to vote. Those living abroad can do so as well.
My DD was in the Peace Corps and all she had to do was request an absentee ballot, and she got one. And sent it back.
So to establish residency for voting purposes, in many cases, you get the drivers license in that state, and can register to vote at the same time (CT allows this…don’t know about Massachusetts).
For health insurance, can she purchase the college plan?