Bestow can only happen from your hand. While the card is in your hand, it is simultaneously an enchantment card and a creature card. When you cast it as a creature, it becomes an enchantment creature. Once the enchantment creature is on the battlefield, it no longer hasis unable to become an "Enchant Creature" spell (I'm reasonably confident that all creatures with Bestow can only enchant creatures). Because of that, the Aura attached to the enchantment creature doesn't go anywhere because the enchantment creature can't enchant another permanent.
Yes. Again, while the card is in your hand, it is simultaneously a creature card and an enchantment card. When you use the Bestow ability, in this instance, the enchantment creature being Bestowed becomes an Aura and ceases being a creature; that Aura spell becomes a creature and ceases being an Aura if the creature it is enchanting leaves the battlefield.