Are epic monsters treated differently than regular monsters with regard to taking damage or being discarded remotely?
Page 6 of the Reference Guide:

Epic Monsters are treated like Monsters for all effects except as described here:

An Epic Monster cannot be defeated by any effect except losing Health equal to or greater than it's toughness.


So, yes to the first part, no to the second.  You can't out-right kill an epic monster with a card ability.  You MUST do damage to it.  Though, if a card does damage, you can use it all day long.
Additionally, with the expansions, you are able to have things that 'Advance the current Mystery'.  If the Epic Monster is part of the current Mystery, you do three damage to the epic monster for 'Advancing the current Mystery'.