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If a prepare spell with one or more targets has no legal targets when it tries to resolve, it won't resolve and none of its effects will happen. Since the spell was cast, the associated permanent will still not be prepared.

Casting a copy of a prepare spell from exile isn't casting it for an alternative cost. Effects that allow you to cast a spell for an alternative cost or without paying its mana cost may allow you to apply those to a copy of a prepare spell cast from exile.

As an effect causes a creature with a prepare spell to become prepared (including effects that state that a creature "enters prepared"), that creature's controller creates a copy of that creature's prepare spell in exile. That copy remains in exile for as long as that permanent is on the battlefield and is prepared. That creature's controller may cast that copy as long as it remains in exile. As they cast it, that creature stops being prepared.