If the first ability returns an Aura card to the battlefield, you choose what that Aura will enchant as it enters the battlefield. If the Aura can’t legally enchant anything, it stays in the graveyard.

A noncreature permanent that turns into a creature can attack, and its abilities can be activated, only if its controller has continuously controlled that permanent since the beginning of their most recent turn. It doesn’t matter how long the permanent has been a creature.

Note that if an Aura is returned to the battlefield this way, whatever the Aura enchants isn’t a target of Starfield of Nyx’s ability, nor is it a target of the Aura card itself. You could put an Aura onto the battlefield this way enchanting a creature with hexproof controlled by an opponent, for example.