Equal and opposite reaction.

There's a law for this. The matter is "pushing" against the ship, it doesn't have to push against anything else.

In fact having an atmosphere to push against actually reduces the effectiveness of thrust due to atmospheric pressure, which must be overcome. Which is why different engines are designed to run in atmosphere versus out of atmosphere.

If you throw a baseball in space you have transferred momentum to that baseball, pushing you back. You will move in the opposite direction (likely spin because you just imparted angular momentum onto yourself since you didn't throw from center of mass)