As the other answer indicates, it can be complicated. These are the simple answers.
Q. Does she claim 1098-T on her return***?
A. No. You claim it on your return, because she is your dependent*.
Q. Does she claim ALL Scholarship/grant money she received?
A. No. She claims only the portion that exceeds qualified educational expenses plus the amount you use (usually $4000)** to claim an education credit.
*Scholarships & grants are considered third party support and not support provided by the student. She, almost certainly, still qualifies as your dependent.
**There 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 1. 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.
***There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. The student cannot be supporting yourself on parental support, 529 plans or student loans & grants. He usually must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit. He cannot claim a credit if he is, or can be, claimed as a dependent by someone else.
