Welcome to TFP!
No, not really. Ideally you should only see water. But often enough there is an air bubble, but it should be a constant size. If you see streams of bubbles, or a roiling frothy mess, then there is an air leak on the suction side somewhere.
Having a visible water level that goes up and down doesn't sound good. That could be a failure to fully prime.
What kind of pump do you have? Have you checked to make sure that the skimmer basket is clear and there isn't a vortex in the skimmer that could be draining air in?