Tiki isn't dying because it probably takes a lot more than just getting shot to kill him - which is true for everyone in the DGM series. As for being exorcised, there's no proof that Allen's sword actually works as it is supposed to (or as he thinks it should). It could be a problem with him.
I don't think the Millenium Earl will fight. He knows it's breaking down, and he's probably just there to poke fun at Cross and steal Tiki - and maybe something involving Lenalee, since she was his target (leave her in the Ark? tell her that she could be the Heart?). I don't think we'll see a fight, though.