If I teleport out of a cave while me and my companions are fighting a creature or npc, does the fight go on?

lol yea, I know, stupid question, but I really cant remember whether it does or not, and I cant really test it now...

Nothing happens in any cell the player is not in. In exteriors several cells are loaded & drawn on screen but any scripts, activators, NPCs, creatures, ect. do anything until the player enters their cell.

No. (I haven't tested it, but I'm quite sure).
There is a MWSE mod, where attacking NPCs follow you through doors/cells, I'm not sure how that would behave.