And why don't you just report the facebook account for fake and that it's mainly dedicated to offend you and your friends?
-Knowing who it is can just cause more trouble than needed and who knows, maybe you are in search of revenge. (doesn't make you any better)
So go on and report the user, as IP addresses and such are mainly kept on their side and has nothing with you to do. So thare is a very low chance of you getting their IP or other information. (This is due to privacy laws, that their forced to protect this data unless you agreed to sharing your data)