Is there a cure for paraplegia caused by a c6-c7 spinal injury?

No cure but. Cervical cord injury is very serious. Common causes are accidents from diving into a pool or whiplash from car accident or hyperextension injury during football. Often the spinal cord is crushed or the blood flow to the cord is stopped so that a region of the cord dies off due to injury and/or lack of blood supply. There is no repair for this. Good rehabilitation can recover what's possible.
Depends. An injury at c67 can range from no nerve problem to total paralysis (also affecting the hands). Complete spinal cord injury (no function below c67) currently cannot be cured, but decompression (taking pressure off nerves in the area) may improve arm function in some. Decompression when the cord injury is incomplete can lead to some recovery of cord function. Recovery depends on severity of injury.