I appreciate all the quick responses to my questions.

If an engaged enemy is removed from the engagement area due to this effect AFTER a shadow card has been dealt, is the shadow card discarded?

Keep that shadow card on the enemy until the end of the combat round, then discard it.

Generally it won't matter, but in some cases the order of cards in the discard pile is important, or some other effect (like another enemy's shadow effect) could force an enemy to engage you, so he should have his shadow card.