Hello,
i understand what you all mean, and i can fly with it, however i wonder what really happens. Certainly forget gravitation and Coriolis effect lol.

"There is only engine torque turning the transmission Narsinha, the mobile axle \:\) which turns the prop one way and the plane (mounted solidly to the engine) the opposite way."

Which is somehow clear, but since the propellor has a tiny mass in relation to the rest of the plane, it certainly turns easier, and that's why the prop rotates, and not the plane. It does have an effect on the plane though, admitted.

"The prop is not solidly mounted to the plane it's free to rotate in its little highly-greased world."

I even understand that lol.

"But constrained to one axis that moves around a bit like Hancock's gravy"

Yeah right. It moves as soon as the plane does any course change. Or do you mean it would move if you'd let it free ? It would stabilize like a spin top then, which, in this case, is really based on the earth's gravitaion.

"The engine turns the prop and the prop turns the work done into friction acting on the atmosphere, leverage."

I can accept that, even with rotary engines the engine turns the prop, be it itself (rotary) or via a crankshaft (in line or v-shaped), ok.

"Which shoves the plane in a counterwise angular direction of rotation to the propshaft's direction of rotation. Leverage is the thing. The propshaft is the transmission device from engine to propellor and the propellor is the transmission device from engine to atmospheric-leveraging"

Yes but that's what i wrote (rotating engines): the engine has to stem itself against something when accelerating - a rotating engine will transfer its momentum to the fixed crankshaft, and tries to turn the plane in the anti-clockwise direction, especially when the engine is heavy, and has a lot of mass.
The mass of a rotating engine revving at a fixed rpm with say 1400 rpm with its fixed propellor will also stabilize level, or better straight flight, acting like a gyroscope.

Greetings,
Narsinha