^^ Wow, that was great to read
I definitely think that the Joker inflicted the scars on himself, because of the very fact that he brought them up each and every time. No one else ever did. Not only does he bring them up all the time, but he even puts draws more attention to them by painting them red. If it was somebody else who inflicted those scars on him, then they would be a sign of weakness, which is something that a man as dominant as him would not want to flaunt.
As to the Joker being schizophrenic, I really don’t think that’s the case. I know Heath called him schizophrenic, but I just can’t believe that. It would be basically impossible for the Joker to pull off the things he does if he did have that particular mental illness. I think the Joker knows very well he is lying, but I also think he has a reason for picking which scar story to tell, although I haven’t figured out what exactly yet.