A correction to my contribution which should be defined better. i.e 'power available over drag'
That's still wrong.
You must compare power with power required, and compare thrust with drag (or thrust required). You can't compare power to drag because they're measured in different units.
Flap may indeed reduce the take-run but often as not will degrade the take-off distance.
Depends on where the takeoff distance is measured to. For a close in point, the more thrust the airplane has, the more beneficial the effect of flaps. For the Part 23 50 foot obstacle or the Part 25 35 ft obstacle, flaps will always decrease the takeoff distance for other than the most underpowered aircraft.
Where you get your idea of the sole reasons for flap I don't know.
Didn't say "sole", but implied "primary", and every aerodynamics book printed describes flaps in this context.
If you insist on continueing with your current practice, as described by you, I hope that you continue to do so no more than 1ft above the runway.
You imply that it's dangerous, which is absurd.
The degree to which flap will generate additional lift and/or reduce the stall speed is type dependant.
Well, of course, but the goal of flaps is to increase the maximum lift coefficient. There is really no such thing as "additional lift", since lift = weight in unaccelerated flight.
Best Rate climb is achieved with maximum excess power over drag.
Sorry, wrong again. ROC = (Power Available - Power Required)/Weight.
Your definition of the forces in a descent are wrong. Albeit that power is not always considered but thrust is.
Nope, it's flawless. Your angle of descent has the equation
Sin(descent angle) = (Thrust - Drag)/Weight
When thrust is zero, you have
Sin(Descent Angle) = -Drag/Weight
Vast numbers of references available upon request.