Yes, grad school is college and is (usually) pursuing a degree.
Simple answer to your other concerns is delete everything related to education, the 1098-T and 1099-Q. You have determined that none of the 1099-Q is taxable nor is any of the scholarship reportable and taxable. You are not required to enter either document.
That said, let's open another issue. You stated " I don't think we got, or qualified for, this credit. There is another tuition credit, in addition to the one limited to 4 years (AOC-American Opportunity Credit). It's the Lifetime Learning Credit (LLC) and is available to Grad students. Your child doesn't have enough income to claim it, on his own return. But, if he qualifies as your dependent, there is loop hole available for you to claim it. It's worth 20% of the tuition paid, up to $10, 000. It's non refundable, so you must have some tax liability. Your child would have to report some scholarship as taxable. But, if he has no other reportable income, the tax is 0, after the standard deduction.
To qualify as your dependent, he, most likely, would have to have been under 24 on 12-31-20.
