Solution for #1

You would impact between the 2nd and 3rd second after the cable broke, so you would want to jump 2 seconds after the break. However, considering the calculations involved, you would probably end up as a heap of screaming bloody mess at the bottom of the elevator shaft before you figured the answer out. Besides, there's no telling if jumping really works.

Solution for #2

About half way. After that, he starts running out of the woods.

Solution for #3

From now until hell freezes over. No telescope yet invented has that kind of magnification. Besides, Alpha Centuri is a star and your friend couldn't get within miles of it without being vaporized.

Solution for #4

Far enough.

Solution for #5

Pretty good! The dice are obviously loaded.

Solution for #6

Apply a tourniquet, and you won't.

Solution for #7

As many as you can carry, if they aren't in dollar-based currencies.

Solution for #8

Who cares? I want to see how that half a boy can eat anything.