One creature or loose object of your choice that you can see within range rises vertically, up to 20 feet, and remains suspended there for the duration. The spell can levitate a target that weighs up to 500 pounds. An unwilling creature that succeeds on a Constitution saving throw is unaffected.
The target can move only by pushing or pulling against a fixed object or surface within reach (such as a wall or a ceiling), which allows it to move as if it were climbing. You can change the target's altitude by up to 20 feet in either direction on your turn. If you are the target, you can move up or down as part of your move. Otherwise, you can use your action to move the target, which must remain within the spell's range.
When the spell ends, the target floats gently to the ground if it is still aloft.
* - (either a small leather loop or a piece of golden wire bent into a cup shape with a long shank on one end)
100.
You probably could, although the funcionality of that is likely largely limited to moving messages/arrows and the like long distances quickly, as catupult has a rather small maximum wieght.
Would another player be able to pull the target affected by levitate down?
Bead of force if the target gets traped cast levitate go under it and lower it so it is right above your head cast thunder wave the enemy is now in the stratosphere
You can use this spell as a low-capacity elevator, by either casting it on yourself, or a small lightweight platform. You have to ride the platform if you want to go more than 60 feet up. It lasts 100 rounds, so you can travel a total vertical distance of 2000 feet, or make multiple shorter trips.
Technically the wording doesn't count any extra weight from things on top of the object, but I would ignore that as an oversight.
No, casting the spell is always an action (unless you use something like "quickened spell")
Actually no. The speed of altitude change is specified and it's only 20 ft per round (6 seconds). If it's dropped on someone it'll just roll off them and gently come down to the ground.