Why is A320's CG optimum position at 25% MAC?
I do not know much about the specifics of the A320 design, but I will try to come up with some general answers to your questions.


  So since CG and aerodynamic center at the same position, there would be no moment arm of lift, so what will be the use of tail plane?


Even if it was the case in the A320 that the CG and AC coincide (I do not know), it does not mean that there is no moment from lifting forces. The aerodynamic center is not the point of zero moment, it is the point of constant moment within reasonable angles of attack. Hence there will be a moment from the lifting force. Assuming CG and AC coincide, the moment generated by lift will not change the total moment on the aircraft. Therefore a stabilizer is still required.


  Also, as fuel burns, the CG shifts rearward, in that case aerodynamic
  center will be in front of center of gravity. wouldn't that mean
  center of gravity is behind the center of pressure?


Not necessarily. The center of pressure is usually for most angles of attack behind the aerodynamic center. Therefore, under the assumption that the CG and AC coincide, the CG can move aft of the AC and still be in front of the center of pressure.