The point of a constant speed propeller is to get maximum efficiency throughout the full range of speeds and power of the aircraft.
How come when I increase throttle, MP increases, but RPM constant because of the governor? What's next after MP increases? Crankshaft connected to cylinder rotates faster to gearbox, and the gearbox eventually lower the rotation so RPM doesn't increase?
If you increase the MP, you increase the power output of the engine, thus the propeller turns faster. The propeller governor (which has nothing to do with a gearbox) detects this, and increases the pitch of the propeller blades. Your blades now have a higher angle of attack, which means more drag, thus reducing the speed of the propeller back to initial value (constant speed). It also means more lift, which gives you thrust on a propeller. You therefore have an increased thrust, which was the initial point of increasing power.
But, I don't understand why do we have to have a "rev-up, throttle back" principle.
Why do we have to do this? Why sometimes we have to select RPM first, then MP?
If you have an important manifold pressure, with low RPM (Low RPM means blades have a very high angle of attack, and thus very high drag.), you will exceed the maximum torque supported by the crankshaft and could damage the engine.
If you want an increase in thrust, you must increase the RPM before the MP so that you do not exceed max torque, and the opposite when reducing power, for the same reason.