Bottom line: you can not claim the tuition credit or deduction because the student is not your dependent.
There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" [QR] in IRS parlance even though they don't have to actually be related). The student is not your QC because she is not a full time student. She is not your QR because her income is too high.
The 1098-T does not have a box for FULL time student, because half time is all that's need for the credit (full time is needed for QC dependency, but determining dependent status is not the purpose of the 1098-T).
Your daughter will be able to claim the education credit, on her return, even though you paid the expenses.
