When units retreat/move due to a combat card, if this leaves no units on one side (often the case when Eldar's lone aspect warrior runs away) damage resolution still takes place for that round.
I think in this case it's no different, damage resolution still takes place for that round, then assuming that one side has some units remaining at the end they are the victor.
This is correct. The battle doesn't end until the end of an execution round, even if only one side has any units left before that round finishes.
It is possible to be wiped out by Death and Despair, but the victim still does enough return damage to rout/destroy Chaos units, or even wipe out the Chaos army.