4, Did flying into a stiff cold headwind improve performance?
Yes, of course it did..
The temperature and air density would make a difference, but I can't believe anyone who knows anything about aerodynamics would be stressed about the whole headwind idea (or even a "stiff" headwind), let alone a group with the knowledge I'd expect from the FAI.
The advantage of the headwind is potentially two-fold though.
First, since take-off is all about airspeed, the stationary plane "at the word go" is already "moving" at the speed of the wind. So the time "saved" is roughly equal to the amount of time it would take the plane to achieve that same airspeed without wind (i.e. a stationary plane in a 30 mph headwind has an airspeed of 30mph; how long would it take that plane to reach 30 mph in dead calm air?).
It isn't about accelerating all the way to take-off speed, it's just an advantage until the plane would have reached the relative wind speed...
The advantage would be very slight, of course, but it would also arguably occur at the point of roll where the plane would be at a poor rate of acceleration?
The second advantage would be due to the shorter ground roll. The wheels rolling along the ground aren't drag-free, so the slightly shorter ground roll would result in slightly less overall drag to overcome. Again, the advantage would be very slight...
One advantage would be gone in the time it takes the plane to accelerate to wind speed, the other would be gone once the wheels cleared the ground.
Which air mass is likely to be more dynamic / turbulent? Calm, or windy? If the wind gives an advantage in take-off, it could also be detrimental if it led to "bumpy" air conditions.