If you mean subtracting out all the stars in our entire galaxy, then the night sky would get a lot dimmer. We'd only see the starlight from distant galaxies and the planets of our own solar system. If you mean just the streak across the sky that is the densest part of our galaxy, then there'd just be fainter and more distant stars in our galaxy to take its place. Regardless, it's very hard to know for sure because we reside in the Milky Way and can't see past it.

You wouldn't see much. Andromeda is the closest galaxy and even that is very faint.