You can out where the CG is on the plane's plans or in the instructions that came with the plane.

If it's a one of a kind type plane you created yourself you're on you own, but you can start with about 10% of the width of the wing back from the highest point on the upper part of the wing.

To answer the second part, yes, all the parts must remain in their respective locations in order to maintain (CG) balance (especially in the air!). Usually one component can be adjustable. Most of us pick the battery because it's being changed out all the time anyway, and it's also the easiest one to adjust back and forth to keep the CG correct. We mount the other parts down so they don't move.

What plane are we talking about anyway?

Goofup