There are many, many children and young people in OP’s situation. There often are no good alternatives. You pick the least damaging, usually for the here or now.
If OP gets into MIT, gets through MIT, prospects will be much brighter. If OP gets through a school like UMass Boston that does have merit money for undocumented students advertised front and center on a website, prospects also likely improved.
In terms of going back to home country and other venues, likely the family has discussed these things and the risks and drawbacks , particularly immediate make them not as attractive. Spending next 4 years at axUS college is probably the best over all choice for OP who is likely still a child right now.
Those I’ve met in similar circumstances did not have better choices than to keep head down to grindstone and get best education and trading.
But as I said above, advice on life choices way outside the scope of this forum. The question at hand is how an illegal immigrant can fill out PROFILE when parent did not file or pay taxes (doesn’t look like he owed any income taxes; FICA and Medicare a whole other story). Also whether this same student can get any aid to go to college, given circumstances