Monkey Business 2 & 3

[Ghost Post]

For number 2 I'd have to say the hunter would aim straight at the monkey. Tranquilizer darts aren't high speed projectiles so they would need to be fired with trajectory in mind like an arrow. Obviously the hunter normally does this since he has bagged quite a few already. As such he normally aims above the monkey so that the dart will drop onto it.
Since he's worked out what the Monkey is doing he fires directly at it so that the dart and monkey drop the same distance. I'm assuming the comment about the monkey being only a few metres away implies the dart will not hit the ground before hitting the chimp.
If the monkey was already on the ground for example at a decent range the dart would hit the ground before it hit the monkey.

Oddly enough for number 3 I would consider there two be three valid possibilities depending on various factors : pulley friction, rope weight, climbing speed.

If the pulley had sufficient friction and the monkey climbed slowly enough then the monkey could ascend the rope without the bananas being disturbed. Both sides of the pulley would be dealing with equal weight so no problems.

If the pulley offered little in the way of friction and/or the monkey pulled hard enough then there would be effectively more weight on the monkeys side so the bananas would go up as well as the monkey.

Finally if the rope were made of something heavy like gold wire and the pulley was low on friction and/or the monkey was pulling hard enough then as soon as the monkey started to climb there would be more weight on it's side which would pull more rope to it's side. Since the rope is so heavy it would continue to feed through until the bananas were stuck at the top of the pulley. At that put the monkey could climb to it's hearts content.

The last option might seem unlikely but a decent 10 metre rope would way far more than 1 kilogram.