What happens if Gildor Inglorion (TBR) is discarded from the encounter deck by a hide test? I have to wait for the encounter deck to be reshuffled to obtain him?

If he's the last card discarded and you have the Neutral event Shadow of the Past you can return him to the top of the encounter deck, but otherwise yes, you just have to wait until the deck is reshuffled. Same goes if he's dealt as a shadow card.

Oh, that's gotta hurt. I'll make sure add those cards to my deck, then.

Luckily all shadow cards get discarded at once so you can choose to discard Gildor last and put him back on top of the deck using Shadow of the Past.

If an enemy is destroyed, is its shadow card discarded at the time that it is destroyed, or do you wait until the end of the combat phase and discard the shadow card then?

Quote

Shadow cards remain on the enemy to which they were
dealt throughout the combat phase. If that enemy leaves
play, discard its shadow card from play. At the end of
the combat phase, discard all shadow cards that were
dealt this round.

Thanks! wasnt in a position to look it up myself earlier, when I posted that.

Next question on this theme: if an enemy with a shadow card leaves play, does the shadow card leave play at the same time (and so I can choose the order) or immediately after (so it must go on top of the discard pile)? We've always done the former, but I don't believe e have any justification for doing it that way.

Pretty sure immediately after, but I have no justification for doing it that way either.

Isn't that quote justification enough for doing it after? When an enemy leaves play you discard its shadow card from play. So there is no way to discard the shadow card first, since the enemy would still be in play.