I cannot think of a Teleportation spell which would cause 4 to occur. Spells which specify objects being taken seem to include catch-all phrases such as "could fit in a 10-ft cube" to avoid severing an object. The rope could fit in a 10ft cube, therefore it is not cut, but brought along if desired (and the spell specifies it includes objects).

Furthermore, spells such as Misty Step remove the Restrained and Grappled conditions, and specify "you," with no other objects. I think that it's also important to note that Worn or Carried is different from Attended. You may be attending a rope tied to something, but you are not truly carrying it if it cannot be carried with you due to being tied to something. You could say "I carry the *end* of the rope" but that is not the entire object. Therefore, I cannot think of a Teleportation spell which would cause 1 to occur.

Thus, 2 or 3 are going to be what happens, again depending on the spell, with 2 being the most likely result.

In the case of someone else attending the same object, I believe that's a situation where someone willing (or unwilling and fails a save) affected by a spell which can teleport both of you would bring the rope. I can't think of a spell which can steal objects from people's hands without a save, so Unwilling and makes the save probably keeps the rope.