Is there a way to block others from using a person's profile page to send them a private message? I know you can block others from making comments on your profile page - does that cover private messages too?

There is no way that I am aware of to block messaging.

If someone is abusing the system and sending abusive mails through the system, you could give that person a warning that their profile will be deleted from the system if they continue that behavior. Then follow through if it doesn't stop.