QIf I select Elana's Prayer with Dark Offering's ability, destroy it, and give my leader defense, can I still play Elana's Prayer's ability?

ANo. By the time your leader gains defense, Elana's Prayer is no longer on your field, so you cannot play its ability.

QCan I play this amulet's ability during my opponent's turn?

AYes, you can.

QIf I have 2 copies of this amulet on my field, and my leader gains defense, does each copy's ability trigger?

AYes. Both abilities will trigger once per turn.