Here's how I would handle it:
Player B would be required to use their Movement to get as close as they could, using their Action to Dash (assuming they can't Dash as a Bonus Action) to close the distance, and their Reaction* to grab Player A or cut the rope, which would either require a Strength(Athletics) roll or an Attack roll against the rope depending on their choice.
The fact that Player B has to roll something to make this happen give tension to the scene and, if they succeed gives a moment of triumph as they save the life of Player A's character. On the flip side, if they fail, it still creates a memorable scene and the players can at least feel satisfied that they got to try to save their friend.
*Can you use a Reaction like that?
The use of a Reaction to grab their ally is a little unorthodox, as there is no specific provision for it, but consider the following:
According to your example, Player B is able to get within 5' of Player A as they are being pulled toward the cliff using their Movement (as depicted by the first arrow). By using their action to Dash, they can get ahead of their ally (as depicted by the second arrow) but by itself, that is not very useful. As a DM who likes to be able to tell my players "yes" when it makes sense to do so, I feel that since the character and the rope will be moving through a square that you now "threaten" you can make an "Opportunity Attack" to grab them or cut the rope. If, after giving this option to the player they thought up some creative way to improve upon it, I would let them try it as long as it made sense that they could make the attempt.
Even if you are not 100% sure of what ruling to make in such a circumstance, as DM you have the right to make up something that makes sense to you, and remember that when you do that, your main goal is to make the game fun. I have found that the best way to do this is to avoid both extremes of 1) Making it too easy, and 2) Denying your players the opportunity to try their plans. The best solution, I have found, is to present a situation that allows the players to make a roll, as long as it makes sense that they should be able to do so, and determine the success or failure based on the result. This way, it feels to the player like the result is due to their character's actions and not the DM's ruling.
The Monk can make a long jump up to 32 feet.
As you quoted,
Long Jump. When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump.
If the monk's Strength score is 16, they would normally be able to make a long jump of 16 feet with a 10 foot running start. Thanks to Step of the Wind, that distance is doubled to 32 feet.
Alternatively,
The Monk can make a high jump of up to 12 feet.
The rules for high jumping state:
High Jump. When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance.
With a Strength of 16, the monk has a +3 modifier and can usually make a high jump of 6 feet with a 10 foot running start. With Step of the Wind, this is doubled to 12 feet.
Best Answer
Yes
Let's start with the general case and some definitions.
Long Jump:
Therefore, in the general case you may absolutely jump as part of any action that involves moving, like a charge.
Looking at your scenarios, Situation 1 is true. You can jump as part of a move. Situation 2 is true, given that there is a square before the enemy, you may jump as part of the implicit move in the charge.
Situation 3 is fun. Case 3a presumes no magical assistance. We consult the following:
Which then simply requires us to satisfy ourselves as to the text of the Charge action:
Therefore, there is no implicit "move action" as subset of charge, the movement is an effect of the use of the power.
Looking at Double Move:
Therefore, the subset of move action that characters normally employ, the walk:
is itself a type of action that comprises a type of movement. A charge is not a walk, and therefore you cannot walk/charge such that you jump on the walk and land in the middle of the charge.
Therefore, if you have to spend a round in the air between an evil guy and a pit, you fall.
You may want to avoid this. Alternatively, grab pouncing armor which, provided a sufficiently high athletics check, allows for jump-charges that exceed your base movement.
Your situation for "needing to charge the guy on the other side of a large pit" is... assuming you must charge them, instead of getting your portable arty to rain death on them and you keep off minions on this side, take a double-move to jump the chasm, then action-point charge. Just... don't fail the jump.