Do we have to pay 1 resource immediately after exhausting him to quest? Or wait until all encounter cards revealed and resolved?

Immediately.

Then when revealed 2 damage to quester ability wont effect him, but his willpowers still there for quest? It looks complicated to me…

Cutievalkyrie said:

If you're talking about Dol Guldur Orcs' When Revealed, Aragorn is still a legit target for it. What his ability does make him immune to are "deal dmg to exhausted characters" (like Necromancer's Reach). He is still questing, but ready.

Thank you. That was exactly where i got confused, now everythings clear to me with u explanation.