I am a 35 year old college student. I had no income in 2020 other than student loans/grants . I have 2 sons age 12. Do I file taxes for the tuition credit and child tax credit?

Maybe.

The money you hear about people getting for just filing a tax return claiming kids requires them to  have some earned income (wages or self employment). Without earned income, they are not eligible for the "refundable" Earned Income Credit or Additional Child Tax Credit.  Both credits are calculated on the amount of earned income you have. No earned income means no "refund". A small amount of earned income means a small refund. The child tax credit does not "kick in" unless you have at least $2500 of earned income.

A child can be the “qualifying child” dependent of any close relative in the household. If you live with someone else, e.g. your parents, it may be better if they claim your child. Instead, you could allow the non-custodial parent to claim the children.  Non-custodial parents are allowed to claim the child tax credit, but not the Earned income credit.

If you are a student, over age 23, and are not claimed as a dependent by someone else (e.g. your parent) you may be eligible for the up to $1000 refundable American Opportunity (tuition) Credit. That credit is not dependent on having either kids or earned income. You must be at least a half time undergraduate student. There's even a loop hole available to claim the credit, if you are on scholarship.

This year, there's the additional issue of the stimulus payments(s). If you are not (and cannot be) someone's dependent, and did not already receive the stimulus, you need to file a 2020 return to get it.  The same, for your children: if they are not claimed as a dependent by someone else, include them as dependent's on your 2020 return for their $1100 each (assuming they're under 17).