You only need PS+/XBL for matchmade activities - so strikes (3 player co-op), crucible (PVP), gambit etc... All camapigns and destinations do not require + reagrdless if you do them with other people or not because they are not matchmade.
You don't have to - everyone that is starting fresh only has to do a basic new intro for new light and then you jump in at 750 power and can start doing just new content if you so wish.i haven't played since Forsaken launched. I played a tiny bit of it. I think i might be better making a new guardian but the thought of having to go through all that again is off putting.