I concur with your explanation. I wrote mine a bit late in the day and should have made the difference more clear. Center of pressure moves, AC doesn't. The part you added about center of moment is also right. And you get the general idea, these are points used in aerodynamic design.

Please try and clarify your use of 2D and 3D terms: 2D/3D distinction is very important in aerodynamics. Airfoils = 2D, Section lift coefficients = 3D. Keep separate, or at least make clear when you are moving from 2D to 3D discussion. This confusion may be why you are mixing in center of gravity with 2D. 2D = no gravity. Center of gravity is irrelevant in 2D aerodynamic discussions.

For a metric ton of real test data on airfoils you want a copy of Abbott and Doenhoff Theory of Wing Sections.

CG impacts lateral directional stability of course. The general topic heading is "stability and control". You might want a decent engineering text; I have Flight Stability and Automatic Control" by Robert Nelson. Pricey, really meant for engineers.