Question: Why would Einhorn kill Roger after finding out that Einhorn used to be a man? Roger didn't know that Einhorn used to be Ray Finkle, only that, as Ace put it, Roger found Captain Winky.
Answer: We don't know that's all Roger discovered, and even so, that could have been the start of Roger figuring out the truth. Einhorn didn't want to take the chance.
Question: How exactly does an escaped male mental patient who's posing as a woman a) work as a police officer without having violent mood swings most of the time, b) acquire money for breast implants and c) avoid a single physical examination that would have exposed his penis?
Answer: Just because someone has been institutionalized doesn't mean they have mood swings. If this was a manic episode (which it appears to be) there wouldn't be any swings at all. Just manic all the time. It wouldn't last forever, but its different for everyone. As for the money, plastic surgery can be financed! and we don't know if s/he had money stashed away beforehand. And for the last question, I just don't know. Not very likely, but some people get through lots of physical testing that shouldn't. Possibly documents were forged? Just speculation on my part.
Answer: The money came from her pro football career, She stole an identity to become a police officer.
Question: How did the guy at the very start know where Ace went? He was back at his car which was parked blocks away, before the guy even realised that the dog had been taken.
Answer: Ace made a very conspicuous exit, either obviously hiding *something* under his shirt, or with the dog's head poking out. So, the guy could have just asked if anyone had seen which way Ace went, and a lot of people would have been able to oblige.
Answer: They appear to be Nanday Conures.