1. When a hero is sent to the discard pile, are all of their resources lost?

I've been playing it that way

2. A discarded hero doesn't receive resources in their pool any more, correct?

3. On the third part of the third quest (Out of the Dungeons) the quest card says that at the beginning of each turn, every player places the top card of their deck face down in front of them. Those face down cards are treated as enemies engaged with the player.

When you defeat that enemy, does your card go to your discard pile or back on top of your deck?

1) Yes

2) Correct

3) Since they are treated as enemies and then defeated, they should go into a discard pile. Since they were originally your cards, not encounter cards, they should go in your discard.