I surfed on the internet for an answer but I didn't find any. I'm taking Aircraft Performance course. I saw that available power for propeller engine is almost constant for every velocity. But I don't know why...
It is a gross simplification, assuming a constant speed prop. If a fixed pitch prop, it is non-linear. Even with a constant speed prop it is not exactly linear.
Lesser factors for power available are the angle of attack/angle of incidence, which will change with airspeed, assuming level flight. Ram air is also a minor factor on some engines.
The diagram you show is a simplification meant to show you that the power is the same, regardless of airspeed, but in reality it varies. How much? I can't say for certain in general, but on one aircraft I collected data on, I recall it varying about 6% in the 20 knot window we were looking at. And to be clear, that was power converted to thrust, not simply power plant power.
available power for propeller engine is almost constant for every velocity
This is because full power is always, in theory, available to you no matter the velocity of the aircraft. In other words, you can always slam the throttle full forward.
The required power is the power that you would need to move at a given velocity (through the air). When the required power equals the available power you would hit your maximum velocity. Above the available power limit when the power required to go a given velocity exceeds the power available from the engine you would not be able to go that velocity (with the exception perhaps of in a dive).