Deductions & credits

OK so the only 1098 info I'm enter will be using the 1098T I received from the community college (on both returns) even though the box info I'm entering will be per our discussion.  Should I though check the box that states at least half time (the community college did not as it was 1 class).  Thanks.

 

There will be no entry on either return naming the university that did not provide a 1098T. Is that correct? It seems a little odd not to be naming that university as that's where my daughter was a full time student in 2020.