The creature card that Nascent Metamorph becomes a copy of is put onto the bottom of the library along with any other cards.

If the target opponent has no creature cards in their library, Nascent Metamorph doesn't become a copy of anything. The cards are returned to that library in a random order.

If another permanent becomes a copy of Nascent Metamorph, it will become whatever Nascent Metamorph is copying. It remains a copy when Nascent Metamorph's effect ends.

If an effect begins to apply to Nascent Metamorph before it becomes a copy, that effect will continue to apply.

If Nascent Metamorph becomes a copy of a legendary card with the same name as a legendary permanent you control, you'll put one of them into its owner's graveyard.

If Nascent Metamorph becomes a copy of an object with a set of linked abilities (for example, one ability that exiles a card and another that refers to the card "exiled with" the object), that link only lasts as long as Nascent Metamorph is copying that object. If it stops being a copy of that object and then becomes a copy again later, the link is lost.