with regards to the rear brakes squeaking while driving then silent when brakes are applied - happens with my front right brakes too but try jacking up one rear corner, taking off the wheel and using a rubber mallet, gently hit the caliper both with the brakes on and off to try to locate where the noise is coming from - found out mine is due to missing springs holding the pads in securely - not an MOT failure but just an irritating noise.