Can I play Dive Bomb if I am engaged with a minion with the guard keyword? If so, how would it resolve?

Yes. Abilities are resolved one sentence at a time, so “[d]eal 7 damage to an enemy” would resolve first. If that damage defeated the guard minion, the second effect, “[d]eal 1 damage to each other enemy” would deal 1 damage to the villain. If the first sentence did not defeat the guard minion, the second sentence would deal 1 damage to each enemy other than the villain and the enemy dealt damage by the first sentence.