RE: question on cg
If the fuel tank is ahead of the CG then you balance the plane with the tank empty. If it's behind (such as in a pusher plane) then you balance with the tank full. So for the large majority of planes you will balance with the tank empty. There is a saying to remember here, "A nose heavy plane flies poorly, a tail heavy plane flies but once". When you balance with the tank empty the plane will become nose heavy when you fill the tank. Flying like this ok because you can still control the plane, and as the tank empties the plane will balance out. However, if you balance with the tank full as the plane flies it will become increasingly tail heavy, which will make the plane increasingly more difficult to control. And the last thing you want to do is run out of fuel and have to dead stick a severely tail heavy plane.
Hope this helps
Ken