Education has a lot of loopholes that the IRS encourages. If your income allows you to claim the AOTC, I would encourage that. Thus:
1. I would make her claim more to max out the AOTC.
2. Yes, she must be your dependent for you to claim the AOTC. I am sure you spent plenty on her!
3. Anything the school requires/ IRS allows. See Qualified Education Expenses - Internal Revenue Service.
4. Whoever claims the student claims the credit.
I am also going to recommend you look at another of my answers for help.
It is sounding like
Tuition, books, fees, etc is probably around $11,500
Scholarship $9700 but claim $2,200 went to room and board, if allowed.
This leaves $4k for AOTC on parents return.
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