yes he spontaniously combusted
Joker never did die in the batman comics.
If you are talking about Batman Arkham City then yes. If you're talking about Batman Arkham Asylum, then no.
Yes he did die sadly.
No, the Joker from Batman is a fictional (non real) character.
In a perfect world.
Actually, Joker does not die at all. In Under the Red Hood, after Batman rescues Jason from the bomb going off, the Joker is then returned to Arkham Asylum. You may be thinking about the movie Batman:Return of the Joker, where Tim Drake shoots him.
When the Joker meets Batman the Joker calls him my dear Darknight.
The episode is titled "Joker's Millions" episode 7 of The New Batman Adventures not to be confused with Batman the Animated Series
The Joker
Batman always wins against the Joker.
Many times (In the movies and TV shows) Batman has threatened to kill The Joker. He has never carried out his threats because it would violate his conscience. There are many comics where Joker does die and I believe there is an alternative comic called 'The nail' where Batman kills The Joker.
It didn't happen in The New Batman Adventures. Look up Batman Beyond Return of the Joker, it's a movie that takes place in the Batman Beyond timeline. Barbara Gordon has a flashback as she tells the new batman (Terry Mcginnis) what happened to them after Tim Drake/Robin was kidnapped and tortured by the joker for 3 weeks. *It shows the flashback in a 10 minute clip*