Do lots of people get mouth trauma, or is it unusual?

Not too uncommon. Depends on who you ask, i guess. Being a facial plastic surgeon, I have seen and treated mouth and jaw trauma arising from atv accidents, bull riding mishaps, car wrecks, etc. If you have a serious injury get evaluated by someone with experience with such problems (facial plastics, ent, oral surgeon, etc).
Very common. Lots of people injure their mouth. Split lips and biting the tongue especially common.
Yes. The mouth is one of the most common forms of entry to our body and one of the organs with the greatest amount of interaction with our environment. It is therefore frequently exposed to trauma and injury.