That was discussed earlier and brought to light two years ago I believe. The definition of battle resolution talks about losing a battle by the numbers and the amount of times each player passes imitative. A character losing a battle by the numbers who can not play anything, once that character is discarded the battle is immediately resolved. So cards like burial and CM were not working in battle anymore only in scenarios of special abilities killing an EC. So you could play a discard and your EC is discarded then you play FA or CM and not give up a lost soul. But if you discard your EC then play CM they get a lost soul then their hero goes back to territory and is then discarded. I believe the scenario that brought this up was choosing the blocker. Opponent would ctb and player would discard that EC then play burial, CM or whatever. No can do.
As for your next question I believe it was a game rule for making one rescue attempt per turn. So EI would go off, they can’t play or initiative passes and you play Grapes, I don’t think you could make another rescue, but I am not looking up the REG on my break at work.