Seriously how can this freshman not even mention The Man Who Laughs, the novel and film that the joker was lifted from? After the actual archetypal stuff had been thoroughly removed from the original character of course, thus making a fun and quirky yet 2-dimensional arch-villain.
What does any of this have to do with the Illuminati? It's never explained once. I guess the people this was made for already know the answer to that. Or maybe the Illuminati have ownership of every symbol and world mythology in existence.