Everflame Eidolon

As Everflame Eidolon's ability resolves, the bonus is applied to either Everflame Eidolon (if it's a creature) or to the enchanted creature (if it's an Aura). If the bonus is applied to the enchanted creature, that bonus won't apply to Everflame Eidolon, even if it becomes a creature later that turn.

If a permanent with bestow enters the battlefield by any method other than being cast, it will be an enchantment creature. You can't choose to pay the bestow cost and have it become an Aura.

Unlike other Auras, an Aura with bestow isn't put into its owner's graveyard if it becomes unattached. Rather, the effect making it an Aura ends, it loses enchant creature, and it remains on the battlefield as an enchantment creature. It can attack (and its tap abilities can be activated, if it has any) on the turn it becomes unattached if it's been under your control continuously, even as an Aura, since your most recent turn began.