For Constantine - I don't think they ever imply that the ability to see angels/demons came from near-death experiences. John was born with it, as was Angela, though she had suppressed hers.

Here's my rationalization for him spilling his guts to Angela, since I find that terribly out of character, too. In my mind, he hasn't told Chas or his other associates that. I can't see John opening up to people about the fact that he hates God because he's going to go to Hell. It seems Midnite knows, but Midnite could have found out from his other connections. Anyway. John tells Angela because:
1-He is about to die.
2-He'd probably like to get laid before he dies, and there's nothing like a healthy helping of pity to increase the likelihood of that.

I also love the Batman. Again - surprising? No. Especially when he's being played by Christian Bale.