Can I or my parents be sued if my dog bites someone?

Yeah. My Mom almost got arrested just because my dog barked at someone.

If you want to prevent it, I suggest you put up a beware of dog, don't pat, don't feed. Sign or even put a muzzle thingy on him/her

Yes, you can. If he/she goes up so someone to bite them, and they need shots, you will most likely be sued, but if they provoke your dog you might win in court