Question: What would happen if a gas separated out into layers like a liquid? What is an example of this?
To answer your question, gas doesn't separate into layers like a liquid. Liquids form layers because the intermolecular forces keep each type of liquid separated from the others - in a gas, these intermolecular forces are negligible, keeping this from occuring.
Sometimes, however, you can find that vapors tend to stay more in one place than another. For example, the fog from a fog machine tends to stay near the floor. However, it's not layered like a liquid is, because if you blow a fan on it, it stays mixed with air. In a liquid, it will tend to go back to separated layers.