I haven’t seen anything to suggest he’s been diagnosed with paranoid schizophrenia. I’ve only seen PTSD and his TBI referenced.
As far as gun laws and mental illness are concerned, only those who have been involuntarily committed to a mental facility via court order or declared insane by a judge (e.g., conservatorship) are added to the national database. All authorized gun dealers are required to run a background check regardless of the state, but not all guns are purchased from authorized dealers. He may have inherited the gun or purchased it from a private dealer. NC doesn’t require a permit to buy a gun and gun owners aren’t required to register their guns.