RE: Adjusting CG on full or half-full tank?
When you get a new plane there is usually a recommended cg to be used as a starting point for the first flight. It is hopefully based on what test flights of the plane have shown. It is largely a matter of opinion - what I say is nearly unstable you may think is way too stable. It is usually very conservative. For convenience the recommended cg is almost always for an empty tank. Otherwise you would have to fool around with a tank full of fuel while setting up for the desired cg before the 1st flight.
If the tank is located near the cg, the cg will not change much from full to empty. Most proifle planes have the tank located in front of the wing, about 10" ahead of the cg. When you balance the plane empty, the cg moves forward an inch or 2 when 10 or so ozs of fuel are added. The plane is bound to fly somewhat nose heavy at first if it is going to be stable at the end of the flight when the 10 ozs of fuel are gone. I fly this type of planes and it is surprising how little the fuel load seems to change the way they fly as the fuel is used up.
The idea is to set the cg such that at no time during the flight the plane becomes more dificult to handle than you are happy with. If you set it at your limit at take off the cg may move back so far as fuel is depleted that is will become more pitch sensitive than you are happy with (or can control) at the end of the flight. The good news is these planes are very easy to land and can work pretty well with an aft cg.
You don't set the cg to make it easy to hover, you set it as far aft as you like and that may make it easier to hover.