Swept wing aircraft, when they stall at the tip, have a tendency to pitch up due to a combination of airflow over the tail changing and the C.G moving forwards.
You may be thinking of the center of pressure moving, rather than the center of gravity. The CG doesn't change unless the load switches.
The aircraft does not pitch up when you reduce power.
Some aircraft pitch up, some pitch down with a reduction in power.
The location of the thrust line in relation to the longitudinal axis of the aircraft in part determines how the application of thrust affects pitch.
An example is a Lake Amphibian. In this aircraft, the engine is located above the aircraft, facing aft. Application of power causes the aircraft to pitch down, and reduction in power causes the aircraft to pitch up.
In aircraft with underslung engines below the long axis of the airplane, application of power typically causes an upward pitching moment.
In aircraft with centerline thrust, or thrust along the long axis of the aircraft, a change in power may mean an pitch up, or down, or no pitch change.
Loss of airflow over the horizontal stabilizer may lead to a pitch up or down, depending on the aircraft, configuration, trim, etc.
Likewise, a change in airspeed causes a change in airflow over the horizontal stab. Most aircraft utilize a negative load, or download on the horizontal stabilizer in flight. As airspeed decreases and angle of attack increases, the angle of downwash or downflow aft of the wing alters. Where download on the horizontal stab decreases, the aircraft tends to pitch down.
Likewise, on some aircraft in which a measure of download in created by propeller thrust or effects of the aircraft power, then a loss or reduction of power means a change in download, and a change in pitch.