If I turn Mirage Mirror into a copy of a creature, and then put it back in the library, is it still a creature until end of turn, or does it go back to being an artifact in the library?
No, it's just an ordinary Mirage Mirror artifact once it's in your library. It won't still be a copy of anything.
The key rule here is:
400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence. There are nine exceptions to this rule:
(None of the exceptions apply. They're mostly about cards keeping track of each other between zones when they need to.)
Generally after something moves to a new zone, it's reset to a fresh state of just being whatever the card says.