So this is probably a stupid question, but here goes. According to the FAQ, threat from the staging area still counts against the players even if no one commits to a quest. So I'm guessing that, additionally, a card is added to the staging area from the encounter deck regardless of whether characters commit to the quest. Right?

Yup, you've got it right.

A question I've had for a while on a similar vein…if you commit all three heroes to the quest and a card with revealed effect (such as the king spider) states, "exhaust a hero" do you still get to count the willpower for all three heroes since they were already exhausted prior to the card reveal effects?

Yes, you're right.