Probably not. Probably not. If the sensation concerns you, see your dentist for evaluation.
I wouldn't think so. I've never heard of that being an issue.
It could. When a person bruxes, they cause forces on the teeth that are transmitted to a ligament that surrounds the root of the tooth. This ligament's function is to act a s a shock absorber. There is build-in space for the tooth to move slightly in and side to side. It is this movement that causes varied sensations on the tooth. The gums could feel as if they need to be scratched.