Since losing landing gear doesn't change the plane's weight, does it change the CG (in the game) when its lowered in a turn fight? (I know it helps reducing the airspeed). Are there any advantages of changing the CG?
<S> Fud
Some planes are designed to make use of lowering gear to slow down e.g. they act as dive brakes on the F4u.
On other planes you may simply go overspeed and rip the gear off!
There should be two effects on lowering your gear. Increase in drag and due to the offset area of the drag a nose down pitch. If the gear retracts in the fore/aft direction then extended it would push your CG forward a hint. If as with most fighters, it retracts sideways, I would not expect any noticable shift in the CG. Other than the effect of drag to slow down, I have not noticed if the other affects are modelled in game, as slowing down also has the effect of a nose drop in most aircraft.
The way you burn off your fuel will affect your CG depending on the tank location. (e.g. losing fuel in one wing tank will shift your CG sideways) Tanks fore and aft will affect your useful CG most.
As a rule of thumb, moving the CG rearward results in a greater sensitivity to pitch making the aircraft more unstable. That can be useful in ACM a you might know, modern fighters are so unstable they need a computer to input the pilots stick requirements. It may make your aircraft more vunerable to spinning as well. A dramatic forward shift of the CG has the effect of converting your aircaft into a lawn dart unless there is a loss of flying surfaces with it such as when you loose your tail!