You got it.
No proof as yet but time will tell.
Eventually he’ll talk, his ego will demand it.
He probably will and that's a good reason to keep him alive now.
Perhaps when the explosives disposal teams get finished, assuming that they are successful without destroying everything in his apartment, information on how and from whom he got the funds to buy large quantities of firearms, ammunition and other stuff will be found. It might be useful to question him about that. Was he, as the "news" says, acting alone? If not, for whom, why and to what end?
At some point, Holmes will discover that he’s not the real Joker. What a rude awakening that will be.