Reveal: Triggers once for whoever put it in territory, if imitated it activates for whoever triggered imitate
Dull: If the blocking player has been determined, only that player gets to search since that player is currently the singular "opponent". Prior to that I'm not sure but it does seem like it would be both
Gain: Same as open hand
Lawless: Triggers only for the player that drew it
Darkness: If it's off your own draw, the one who drew it. If it's put in play by opponent, not sure but I would lean towards the player who's deck it came from
Exchanger: Just the player who drew it
I don't actually know if these are correct, these are just my interpretations of the abilities.