The Crow/WMG

Albrecht was formerly a cop in Gotham City, or some other city home to superhumans.
Explains how easily he goes along with the idea of a guy coming back from the dead.
 * Also, in Tim Burton's Batman, Commissioner Gordon addresses a young black cop as "Albrecht".

All the supernatural stuff is just an hallucination.
In the comic, at least, the circumstances of Eric's death and ressurrection are a lot more ambiguous. It's possible he was only clinically dead for a short period. His visions of the afterlife and apparent inability to feel pain are simply due to one or more factors including brain damage, drugs and/or simply going insane with grief and anger.

The various Karas warriors are incarnations--or even a sort of "sub-species" of The Crow.
"Karas" actually means "raven" in Japanese, and the supernatural elements, including the near-death nature of the protagonist, seem to match up. The fact that every city has a Karas may hint at a different but related type of power.