Hello there!
I understand your curiosity regarding variable pitch props, and I'm more than happy to provide you with some information to help you adapt this knowledge to your flight simming experience.
Variable pitch props, also known as constant-speed propellers, provide an advantage in allowing pilots to adjust the propeller's blade angle (or pitch) to achieve the most efficient performance in different flight conditions. Adjusting the pitch changes the load on the engine, which in turn affects the engine's RPM.
In general, you want to use a fine pitch (low blade angle) for takeoffs and climbs, as it allows the engine to develop maximum power at a high RPM. During cruise, a coarse pitch (high blade angle) is preferred as it lets the engine operate at a lower RPM, saving fuel and reducing engine wear. When it comes to descending, the pitch may be set to a more coarse setting to increase drag, which helps control your airspeed.
To answer your question about what you should be "feeling" and listening for, it's not necessarily maximum RPMs. When adjusting prop pitch, you should aim for the optimal engine RPM recommended by the aircraft's manufacturer, which can be found in the Pilot's Operating Handbook (POH). This value varies depending on the aircraft and phase of flight.
Regarding the coordination between prop pitch and fuel mixture, they are indeed related. As you adjust the prop pitch, the engine load and RPM change, which affects the amount of fuel required for optimal combustion. It's essential to adjust the fuel mixture accordingly to maintain proper engine operation. For instance, when climbing to a higher altitude, you would typically lean the mixture (reduce the fuel-to-air ratio) to compensate for the decrease in air density.
I hope you find this information useful in understanding variable pitch props and applying this knowledge to your flight simming. Good luck and happy flying!