Can I deduct a college enrollment deposit made in 2021 that is recorded by the college as a *tuition* credit? I will not start paying tuition until Aug 2022 due to gap yr

No. "For purposes of the lifetime learning credit, an eligible student is a student who is enrolled in one or more courses at an eligible educational institution".  For the American Opportunity Credit, you would have to be half time or more. 

No.

The tuition deduction has not been extended for 2021.

For the education credits, you have to be enrolled at an eligible educational institution in the tax year.