Of course he can- he is an ordinary human being who ages and will eventually be too old for fighting. Unlike Superman, Batman is vulnerable and has no superpowers. He can get shot, stabbed, poisoned, and electrocuted.
batman doesn't die
No.
No
Stephen Batman died in 1584.
Yes, he does die in batman begins because of the train crash.
Assuming there's no kryptonite Batman, obviously
no
no
Batman's parents died in Crime Alley when a criminal shot them.
In Batman R.I.P; Bruce doesn't necessarily die, only looses his memory of ever being Batman. (I'm sure there's more, but that's all I've got.)
Yes he did die sadly.
If you are talking about Batman Arkham City then yes. If you're talking about Batman Arkham Asylum, then no.