Yes, your parents can claim you if you are under 24 and a full-time student for at least five months.

Full-time student is whatever the school considers "more than half-time".  There's a check box on the 1098-T

The education credit follows the exemption regardless of who actually made the payments.

If you are claiming your own exemption you get the credit.

If your parents are claiming you then they get the credit.