Workset1 is the original workset, you can't delete it, not without using Detach from Central to discard all worksets. It is special in that Autodesk has recommended in the past that we do not remove it. I don't know if they still stand by that anymore but I observe that practice and don't rename it either. If it gets renamed I find users are confused if it can't be eliminated later.
Linked models have two workset parameters, one for each instance (if there are more than one copy of the link in use) and one in the linked file's Type Parameters. When these are set to different worksets you get what you describe.
The project base and survey points are no longer assigned to Workset1, they have been changed to Project Info (a Project Standard) so they can't be deleted inadvertently if they are assigned to a workset that can be deleted (which happened at least once).