joker dies and batman gets cured of his sickness. And harley quinn has a "suprise" that you will see if you listen at the end of the credits. (Hint: Hush little baby)
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Talia al Ghūl dies at the end of Arkham City. However her body does not appear at the end of the game implying that the League of Assassins took her body to place it in the Lazarus Pits.
He's still beat up from when Batman kicked his buttocks and from when he changed back to normal at the end of the the first Batman Arkham Asylum game.
It is a see-saw. If you are facing the gate in Arkham North, turn to your left and search the bushes. You should find the see-saw with hats on each end
In the end of arkham asylum, joker was defeated in his titan form and later returned to normal. He was still in arkham asylum when you fought, so he just had to be captured by police. Harley Quinn escaped the asylum's police and broke out the joker when he purposely got solitary confinement by digging a guy's eyes out with a spoon. They eventually had to swim to the shores of Gotham, but they found that the half they were on was changed to arkham city.
It is at the north end of the city at the right of the Art Hall.