You have obviously over analyzed this much more than necessary. You are
correct about nearly all of it. To answer you questions:

Yes as the RPM Decreases so does the Horsepower.

A constant Speed prop = constant RPM which = Constant Horsepower
(almost) The engine does not know that the airspeed has changed it is
only delivering power to the prop hub.
While the Horsepower delivered to the Propeller will be
constant the effecincy(sp) of the propeller at different speeds and
blade angles will vary some so the actual thrust produced will vary
some.

Yes I believe the constant speed prop results less energy lost across
the airspeed changes, but I doubt it is enough to be noticable.

I think the weight of the airplane has more to do making the maneuvers
easier to do. This is because you have more kinetic and potential
energy to work with through out the maneuver.


Brian