1.If the Hero is exhausted at the same time that the Minion/Monster uses it's last combat card, then the Minion/Monster wins the battle, right?
If the Minion/monster isn't killed, Sauron gets to allot influence according to Wisdom, etc. If the enemy survives, it won.
2.There's no replenishing of the "combat-hand" in a combat once the original hand is drawn at the beginning,
right? What I'm trying to say is that the only way to get new cards in the hand, for either combatant, is to finish combat & start a-new, later, (just one hand drawn for each battle) right?
After using Agility to draw cards, no, no drawing cards normally. Eleanor has cards that allow her to draw more cards. And for Heroes, their hand of course has to last the entire turn, after they draw it during the Hero Draw Step, through every Move and combat, they get no "combat hand" draw at the start of a combat, only may draw more according to Agility, Minions/monsters get a combat hand.