I noticed this a lot of times too, and it kind of annoyed me as well since it made stable orbits around moons practically impossible. I think that this is because of the gravitational effects of other nearby bodies, since SpaceEngine uses n-body physics(realistic) unlike KSP.
Yep. You can see the same effect in Orbiter, when orbiting the Moon, for instance. Even more profound for the Galilean moons. Orbiter also has a little display telling you what percent contribution to the local gravitational field comes from the object you're closest to. Basically a quick way to visualize your location within the Hill Sphere. I really liked that; could be a cool feature to have in SpaceEngine.