> Like, how we orbit the sun and turn in different ways, why would we not see different parts of space in the sky throughout the year?

We do. Look up in winter and you see the winter sky, the set of constellations that are on that side of the sun. Six months later when the earth is on the other side you see the summer sky, the set of constellations that are on the other side. If we could see stars on a summer day then we would see the winter sky in daytime (and the summer sky at night of course). As the earth orbits the sun, the dark side of the planet provides a view of the surrounding space that pans a little bit every night.