When a unit dies in a marsh, does the opponent get a victory banner?

A unit passing a marsh and loses the last block, does the opponent get a banner?

Edit: Another question - When a warrior charges, he moves 2 hexes and MUST battle, but what if the enemy unit is eliminated before the warrior's close combat?

yes. Is there a reason you think this might not be so?

Nothing happens. The warrior must move adjacent to a unit if it wants to move 2 hexes, but if all adjacent units are eliminated before it gets to attack, such is life.