Thanks for the second part, lol.
I know he's never been a killer, well not a cold blooded one, in the comics. But he has committed crimes and is so narcissistic that he can't help but to leave a clue at the seen incriminating himself (to those savvy enough to decipher it...usually only the Batman can).
His motivation would be to further incriminate the Batman to keep the police and Batman busy, by having the police continue hunting him and Batman continuing to run. This would allow him to be more able to take over the crime in Gotham City. This way, we can combine the Riddler of current comics, where he is portrayed as a reformed private investigator who helps the law, and the Riddler of a story like Hush, where he is the mastermind behind it all. I want to see him as an investigator brought in by the police to discover Batman's identity. While spending his time at GCPD he uses their resources and his proximity and intimacy with certain officers to easily get close to them and to commit the murders and leave the evidence that implicates the Batman.
Only the Batman, when putting all the clues together can see that there is a larger scheme at work here, and discovers clues that allow him to know that this killer, this Riddler, is the true culprit but that he has intimate knowledge of what happened to Harvey Dent.
-R