Is stuttering after a head injury normal?

Not Necessarily. Assuming that there were no problems prior to the head injury, various speech problems can occur after this type of injury, but it depends on the area of the brain that is affected. It is always a good idea for a person to be fully evaluated after a head injury for all kinds of possible problems related to learning, communication, and even personality or behavioral changes.
Depends. There wasn't stuttering before the injury, correct? If the temporal lobe of the brain sustained an injury after the trauma, stuttering could possibly be a consequence.