And that's why you exercise the CSU before take off. If you don't you will have cold oil in the prop control system giving you sluggish prop control as you feed in the power.
Not necessarily.
That's why I do a double take on looking at the props of museum aircraft. The props should always be on the fine pitch stops unless feathered.
Not necessarily. Depends on the propeller system in use.
Simplistically variable pitch props do whatever they have to do to maintain the engine RPM that you set on the lever in the cockpit.
Not necessarily. Constant speed propellers do that. Not all variable pitch propellers are constant speed.
...through the magic of oil, gravity and rotational velocity, the prop will maintain the RPM set by the pilot...
Gravity plays no part in the process. Oil pressure, spring tension and compression, aerdodynamic twisting force, and centripetal force, however, do.
The blade angle is automatically controlled by the prop governor, and the cockpit power lever(s) control the amount of fuel being fed to the engine, and thus the power output.
These sorts of setups have several safety mechanisms to stop the prop blade angle getting to low and thus having the airflow driving the prop to any large degree.
In some engines that's so, but others not at all. You're describing a negative torque sensing system which helps prevent the prop from absorbing slipstream energy and therefore imparting the resulting drag to the airframe. This certaily isn't the case with all turboprops, and not at all with large piston mounted propellers such as on radial engines. In fact, in many propeller installations, regardless of piston or turbopropeller, when the power is retarded enough that the engine is no longer driving the propeller, the propeller will be driven by the slipstream, and RPM becomes a function of airspeed and governor setting, rather than governor setting and throttle/power-lever position.
Try seeing if a Hamilton Standard hydromatic propeller modulates to reduce drag in a negative torque sensing mode some time. It doesn't. Doesn't even feather on it's own...it must be driven there by a dedicated pump.
On the ground, both the blade angle and the fuel supply are directly governed by the power lever(s).
Not necessarily.
Think of the propeller as a wing aerofoil that gives its best lift/drag ratio at a particular angle of attack.
This will transform to a best thrust/torque ratio.
A fixed pitch propeller will get a progressively lower angle of attack if forward speed is increased while RPM is held constant. So to absorb the full torque of the engine, the pitch must increase as forward speed is increased to maintain a constant angle of attack.
Not necessarily. As airspeed increases under constant power, pitch increases and for a given section of blade angle of attack increases to some degree, not decreases; both to take advantage of the power absorbed by the engine while maintaing a constant RPM, and as airspeed increases the blade angle must also increase to prevent an overspeed condition.