For spells and effects which last "for the duration of the battle", do they only apply to the first pit fiend you roll against, or all of them?

The first one only. If they attacked in a group, then it would be different, but you should class each Pit Fiend as a separate battle.

But you *do* fight them all (separately) on the same round, right?

Yes, one at a time. Until you lose/draw that is. Then you would carry on next turn.