Do I say yes or no to “Did you pay for any school supplies or books?”, if I did pay for all my supplies but was reimbursed by my scholarship later on? That would be no right?

Actually, you answer yes.  TurboTax (TT) is trying determine of any of your scholarship is taxable (in addition to trying to determine if you qualify for  a tax credit or deduction). Scholarships that exceed qualified expenses are considered taxable income.

Be aware that t

here is a tax “loophole” available. The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his return. That way, the parents  (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship.  You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.

Using an example: Student has $10,000 in box 5 of the 1098-T and $8000 in box 2. At first glance he/she has $2000 of taxable income and nobody can claim the American opportunity credit. But if she reports $6000 as income on her return, the parents can claim $4000 of qualified expenses on their return.