Re question #27: I wasn't trying to say you always climb faster in a headwind. I was talking about a wind gradient. (Yet another use of the the term "gradient"!)
I agree that I'm adding another "twist" that wasn't stated in the original question, but a headwind gradient (increasing headwind with altitude) absolutely does boost the climb rate. So does a reverse tailwind gradient (decreasing tailwind with altitude) but this is much less common. We climb through some amount of headwind gradient on nearly every takeoff.
The same headwind gradient that helps the climb rate, also increases our sink rate as we descend down through it. This is a very real effect that demands some extra airspeed for a safe landing approach when the gradient is strong. So that we have enough energy to flare, ie. arrest the high sink rate.
Descending through a tailwind gradient, on the other hand, will reduce the sink rate. This can add to your woes if you are accidentally landing downwind, in which case there are two different factors tending to carry you far down the runway-- higher groundspeed than you may be used to, and also a lower sink rate.
These effects are real enough to be easily detectable in light plane flying. Near the ground is where the largest gradients usually exist. Are there real-world cases where you could measure a significant change in climb rate due to these effects when testing over intervals of 1000 feet or more, starting at least that high over the ground? I'm not sure...