Poison and fire, no, they do a % based on the target's hp

Bombs are based on the attacker's attack stat, unless otherwise stated. Komidus's bombs are based on his hp, but off the top of my head I think he's the only exception.

I don't *think* crit affects bombs, but I'm not certain of that.

Crit does not effect bombs no.  With the exception of Shazar needing to Crit for it to be a 1 turn duration instead of 2.