What are the effects of camber location in an airfoil?
[Does] the location of the camber in the MAC's airfoil correspond with the aerodynamic center?


No.

The aerodynamic center is where the additional lift force from a change in angle of attack can be summed up. Since camber only determines the lift portion that is independent of angle of attack, changing the camber will not influence the aerodynamic center.

For a high aspect ratio wing in subsonic flow, the aerodynamic center is at the quarter chord position. With decreasing aspect ratio this point moves slowly forward until it arrives at the forward tip for a slender body.

Also, strictly speaking, there is no "location of camber" — camber is distributed over the whole chord. What you probably mean is the highest point of the camber line, but that point has little aerodynamic significance. The local curvature of that line is much more important.


  Also, does that affect the moment coefficient?


Yes.

Generally, the more an airfoil is cambered towards its rear end, the higher its pitch moment coefficient will be. This is called "rear loading" and is used in order to combine decent thickness with good lift in transsonic airfoils. You can use the lengthwise location of the highest point of the camber line as a guide how high the moment coefficient will be.


  And what about a high speed aircraft (M>1)?


That depends on wing sweep. Normally, aircraft designers try to keep the wing's leading edge subsonic over the full speed range. But I guess you wonder how the camber will influence a wing's performance once it moves at full supersonic speed. Well, the bad news is that camber will drive up wave drag without any influence on lift. Supersonic aircraft, therefore, use thin airfoils with very little camber, and the camber they have is only there because it helps in subsonic flight.