You've got several variables working at the same time.
ADL does two things depending on your settings and how you post process. It reduces exposure by 0, 0.3, 0.7 and 1.0 stops for Low, Medium, High and Extra High. This is a straight exposure adjustment from whatever mode is being used. It also applies a curve to the image to restore a near normal exposure for the scene. This second part is only read by your post processing software if it reads and uses camera settings - the Nikon programs use the settings. Adobe family programs do not use the camera settings and simply have an underexposed image. If you use Capture NX2, you can adjust the curve on NEF files in post processing.
Matrix metering is just fine but there are situations where it does not work well. Matrix attempts to balance the background, so if your subject is well lit and crosses backgrounds with bright areas or shadows, the exposure will be adjusted accordingly. Your AF sensor selection will increase the emphasis on that part of the frame. In the case of changing backgrounds, manual exposure probably works better since your lighting on the subject won't change.
Center weighted metering will place more emphasis on the center of the frame rather than the background. It will help with changing backgrounds, but not with changes between light and dark uniforms.
Spot metering probably won't work for a moving subject. It depends too much on putting the AF sensor on your subject.
Manual is just fine if the subject is in the same light all the time. On partly cloudy days with subjects moving in and out of varied shadows, manual will not work very well and center weighted or matrix is probably better.
I don't think it is a camera or lens problem. A stuck aperture normally affects every image. The camera is probably okay. It is possible to select bracket by mistake.
My guess is you need to pay extra attention to what settings give you a good exposure with no blown highlights. The highlights setting in playback mode uses "blinkies" to warn about blown highlights.