All attackers are chosen at once. You can't attack with Ahn-Crop Champion, untap a tapped creature, and then attack with that creature.

Untapping an attacking creature doesn't remove it from combat.

If you attack with two Ahn-Crop Champions and exert both, each will untap the other.

You can't exert a creature unless an effect allows you to do so. Similar effects that "tap and freeze" a creature (such as that of Decision Paralysis) don't exert that creature.

If an exerted creature is already untapped during your next untap step (most likely because it had vigilance or an effect untapped it), exert's effect preventing it from untapping expires without having done anything.

If you gain control of another player's creature until end of turn and exert it, it will untap during that player's untap step.

All cards in the Amonkhet set that let you exert a creature let you do so as you declare it as an attacking creature, as do some of the cards in the Hour of Devastation set. You can't do so later in combat, and creatures put onto the battlefield attacking can't be exerted. Any abilities that trigger on exerting an attacking creature will resolve before blockers are declared.