^^^Well stated.

If you sense the threats are serious, I'd report them. If it's in writing, the threats, at least send that off to Facebook. There's a line that needs to be drawn. Whatever the threat, slander or of a physical nature, it's harassment, and such behavior is better off addressed asap.
Sorry your feelings are hurt, it's painful when dealing with it. Remember, just like IRL, not all around are the bully. Just usually, if you don't stand up for yourself, it could escalate. Not everyone knows to defend or how, and it is a better feeling to take your own initiative.