Foe Requiem increases the damage of summoner and scholar dots, white mage's holy and all of black mage's spells. Since it's applied to the enemy itself, anybody attacking benefits from it as long as they fit into those criteria. The more mages there are, the more foe requiem helps. You can burn the hell out of ST bosses with it. Foe should pretty much always be used at the start of a boss pull.

Mages' Ballad should only be used when a healer has about 25% MP but this should never happen if they aren't constantly raising people or overhealing. But you should always play ballad right after a healer is raised.

Army's Paeon is almost useless. Turn 8 is the only fight in the game where it's mandatory. Otherwise only useful if you screwed up your invigorate uses and became TP starved.