1. Agree with megamanlan, as long as the character is unique. Generic characters can enter any number of battles, and do not even have to be 'reset' by hitting hand, deck, or discard anymore.
2. Agree with megamanlan, I'm pretty sure this is how it has been ruled. Just note that if you make a successful rescue, you may not make another rescue attempt until each opponent has a turn.
3. I'm actually fairly certain it should be discarded. My basis would be placed in the rulings regarding Assyrian Survivor. If he is hit with Counsel of Abigail and is bottom-decked, he still loses and his special ability places him in opponent's LoB. The SA on Spear was not negated nor interrupted (as it is ongoing, an ITB and return would not allow the SA to be active after it returns to hand), it still happens. Wherever it ends up, its SA is still going to trigger, so it is found (wherever it is) and discarded.