How does the pitching moment change as the speed of A/C approaches critical Mach number?
Yes most aircraft which operate in the transonic zone experience a nose down pitch with increase in speed. The two main causes are : 


Rearward movement of centre of pressure
Because of supersonic acceleration at higher speed, pressure continues to decrease past the 50% chord point, thus increasing the amount of lift produced by mid chord part of wing.
Modification to airflow over the tailplane
Most tailplane work in a region of downwash from the mainplane, in case of swept aircraft the downwash can be considerable. The formation of shockwave on main plane modifies the flow such that the downwash is reduced and this will pitch aircraft nose down