CG
There is a range of usable CG locations. That range is about 5 to 7 percent of the mean aerodynamic chord. The best CG location within that range depends on the purpose of the aircraft, the flying style and skill of the pilot. The location of that range of usable CG locations depends mainly on the tail volume coefficient. The larger the tail volume coefficient, the more aft the range. The horizontal tail volume coefficient is the tail moment arm length (expressed as multiples of the wing's mean aerodynamic chord) times the area of the horizontal tail (expressed as a fraction of the wing area).
There are secondary considerations that affect the location of the usable CG range only a little. A large or unstreamlined fuselage and its appendages slow the flow over the tail and render the tail area a little less effective. The aspect ratio of the tail is another consideration with high aspect ratios being a little more effective for their area.
In full scale aircraft the aerodynamic centers of the wing and tail do not shift appreciably and the neutral point (which is the most aft usable CG location) is stable with changes in angle of attack between the upright and inverted stall angles of attack. However, at model reynolds numbers the aerodynamic centers move around a little with angle of attack. This instability of aerodynamic centers is caused by the waxing, waning and shifting of laminar seperation bubbles as well as variations in thickness of the boundary layer with angle of attack.
A plot of coefficient of lift vs angle of attack is normally a straight line. However, some thin symmetrical airfoils used for tail surfaces have a kink in that straight line near zero angle of attack. The kink is caused by the shifting of the laminar seperation bubble from one side of the airfoil to the other. The symptoms are not unlike deadband in the elevator servo.