Nice. I had that as one of my solutions (but with an approximation of 1°C every 100m).
Q3: Nice methods!
Q9: True, but… what if no-one remembered? (Perhaps a bright light caught everyone’s attention instead…!)
Q12: Correct! (Well – more or less. The exact distance from the South Pole is actually [1km + (R * arcsin(1km/2πR) / 1rad)], where R is the radius of the Earth, but I think that (1 + 1/2π)km is close enough.)