Does Enchant Creature Target?

Thanks! Yes. Guard Duty, like other auras, targets the creature it will enchant when it is a spell on the stack.

Does enchanting a permanent target?

When you're casting the enchantment as a spell, yes. When the enchantment is brought into play in some other way, no. (Note that while hexproof and shroud only prevent targeting, protection prevents enchanting specifically.

Do enchantment auras target creatures?

Creature spells and other permanent spells (except for Auras) never have targets. A heroic ability triggers only when the creature's controller casts a spell that targets it, not when any other player does.