Both banana and monkey experience the same acceleration since gravity causes all objects to accelerate at the same rate regardless of their mass. Since both banana and monkey experience the same acceleration each will fall equal amounts below their gravity-free path.

How should the hunter aim to hit the monkey? The monkey starts a vertical distance h above the hunter, and the horizontal distance between the monkey and hunter is d. The origin is the hunter. That exactly matches the monkey's position, so the bullet will hit the monkey when the hunter aims the rifle at the monkey.

In other words, if there were no gravity, the monkey wouldn't drop, the dart would hit the monkey because the shooter aims directly at the monkey. Now, since the gravity has the same effect on the monkey and the dart, "turning on" the gravity makes no difference in the result.

So they fall the same distance in the same time. The monkey falls from the tree, while the dart falls the same distance from the straight-line path it would have taken in the absence of gravity. So, if the zookeeper aims at the monkey initially, the dart will always hit the monkey.

Therefore, the dart will always hit the monkey, no matter the initial speed of the dart, no matter the acceleration of gravity.

Yes, the bullet will hit the monkey. As at the same instant when the hunter fires the bullet, the monkey also drops. Now both, bullet and monkey will experience the same downward acceleration due to gravity 'g'. Therefore, it will lower the height of both bullet and money, by the same amount.

The vertical acceleration due to gravity is the same. Therefore, if you throw a banana horizontally at a monkey in a tree, the moment you release it, it will start to fall at the same speed as if you had simply dropped it. That's why you should aim directly at the monkey.