UMass Boston actually welcomes Undocumented students to apply and has merit scholarships available. There are likely other such schools.
As for the CSS Profile, it might be a good idea to talk to the MIT financial aid office for advice and direction in how to complete that form.
There are many illegal residents working and attending college here in our country. How they prepare for the future, their children’s future really goes into difficult avenues beyond the scope of a College advice board.