A) In an airplane with a piston engine and a constant-speed prop, flying at some given airspeed with the manifold pressure and RPMs in a typical cruise configuration, would it ever happen that increasing the prop RPM higher and higher without moving the throttle would at some point actually start to decrease the thrust and power delivered to the airframe?
Assume no electronic engine controls such as FADEC.
I'm imagining a case where flattening the pitch of the prop blades would decrease the thrust and power delivered to the airframe, because the prop blades would be meeting the local airflow at a lower angle-of-attack, despite the increase in RPM. I guess an extreme case would put the prop blade at a small negative angle-of-attack to the local airflow, so that the prop was acting to drive an increase rather than a decrease in the engine RPM-- obviously this would increase the RPM but would decrease the thrust and power delivered to the aircraft, at least in the forward direction.
B) It occurs to me now that such a thing might happen at lower throttle positions but not at higher throttle positions. So a second part of this question is, on final approach with the throttle at idle, is it true that the prop exerts more of braking effect on the airframe when the prop lever is set for high rpm than when the prop is set for low rpm?
C) And the third part of this question is, for some given airplane cruising at some given airspeed with RPM and manifold pressure initially "square", what is an example of the highest initial manifold pressure at which we might find that advancing the RPMs higher and higher without changing the throttle setting might eventually cause a drop in the power delivered by the prop to the airframe? Or is this something that would only happen at very low power settings, such as would be used in a descent, and would never happen at any power setting capable of sustaining level flight at any airspeed? (This is basically a more refined version of part A.)
The intent of the question is that the advance in the RPMs is intentional and goes no further than the max allowable RPM of the engine and prop. Clearly a "runway" prop would be an extreme example of these dynamics but the question is intended to be constrained to the normal allowable operating envelope of the prop and engine.
Some related questions and answers on ASE--
Manifold pressure vs rpm vs power obtained and more about constant speed prop
On a constant speed propeller, how is blade pitch related to airspeed and efficiency?