I'll answer the first part - If the parent's actually claim the child, no, the student can not claim an educational credit.  If the parents' choose not to actually claim the child, yes, the student can claim the educational credit (be sure to still indicate that they CAN be claimed as a dependent, but are not actually being claimed), BUT will NOT qualify for the Refundable portion of the American Opportunity Credit.  So it would only be used to offset income tax.

As for the 1099-Q, it can be a struggle to figure out out to fill things out in the software to make it behave.  Are you entering it on the parents' return or the student's return?  What software are you using?