Would any of these constitute a help action or a grapple?
The simple answer is no. To help someone, you have to put some effort in it, and this will cost you a standard action, and all of your scenarios leave you without one.
Also grapple is no help hier, since it needs your standard action, too.
Note also that the grappled condition states:
PHB p. 290: The condition also ends if an effect removes the grappled creature from the reach of the grappler or grappling effect, such as when a creature is hurled away by the thunderwave spell.
Therefor the pull on the robe will simply end the grappling.
Now lets have a look on your suggestions
Can Player B us their action to move up to the Player A and a free action to grab/hold onto them?
RAW: no, since hold and grab are standard actions
Note that some characters (for example rouge/monk lvl 2) can use a bonus action to do a dash, therefor they could do a move, dash and help on the same turn. There are some spells which could help, too.
Can Player B run up and throw themselves on top of Player B?
I don't know any rule not allowing this. I would allow a player to drop to the ground for free as part of her/his movement, since it is less effort than jump and land on your feet.
Lying on top of Player A could help you by increasing the wight the rope has to pull on. But I would rule, that Player A has disadvantage on strange saving throws on withstand the pull, since she/he is hampered in his movements by a body lying on top of her/him.
Can Player B move in front of Player A and just stand there to try to stop them from being pulled by?
No, a creature pulled by don't allow you to use your reaction. Neither you get an opportunity attack (neither Player A is hostile nor Player A uses a move action or reaction, and both are required) nor it would help you anyways (since a grapple wouldn't stop the pull as RAW states).
Can Player B run ahead and grab the rope as a free action?
You can get your hands on the robe as a free action as the 'Interact with Objects Around You' Table on PHB p. 190 suggests. But to get a firm grip on the robe and pull it with force is much more than simply pick up an light object. In my opinion it therefor would have the cost of a help action.
But as a GM I would allow it, if Player A would die otherwise.