hogwarts will have to open at some point because she expressly states someone comes back as a teacher. if it was closed forever that wouldn't happen.
and i can't see harry being a horcrux for one more good reason. when voldemort possesses harry at the ministry of magic, he tells dumbledore to kill him [harry]. 7 horcruxes he may have made, but it is highly unlikely that he would be so cavalier about them as to volunteer to have them destroyed.