If player A controls Pandemonium when a creature enters under player B's control, player A controls the triggered ability even though player B chooses the target and chooses whether to have the creature deal damage, which could be important if multiple abilities controlled by multiple players trigger.

The triggered ability does not check the creature's power until the ability resolves. If the creature is not on the battlefield when the ability resolves, it does damage equal to the power of the creature right before it left the battlefield. This means that if a creature enters which can destroy itself as an "enters" ability, the order of resolution of the triggered abilities does not matter.