@jasonmoon,
1) Terminal velocity is where the egg no longer feels acceleration. That is the point that the air resistance matches the gravity. Force = mass x acceleration so:
9.81 m/s^2 x 0.1 kg = k v
v = 0.981/k
2) If you don't want to use differential calculus on this one, assume the earth egg is at terminal velocity and find out how long the moon egg has to go to reach the same velocity. The moon egg velocity = a t = 1.62 t. Set that equal to the terminal velocity above and you get t = 0.981/1.62/k = .605/k seconds.
The formula for distance traveled is H = 1/2 a t^2 = (0.5) (1.62) (.605/k)^2 =.296/k^2
3) The thicker the air, the greater the drag due to air resistance so you would expect k to be higher at sea level than at high elevations where the air is thin.