I think hiding the link is a typical "simplification problem", many Microsoft products suffer from. This is a problem because the alerts about changes in items do report in the underlying column order, not in the content type column order.
You can construct the URL by going to the formEdt.aspx page, e.g. select General Settings, and replace the ...
You cannot create columns at file / folder level.
Columns can be created at document library level or content type level.
Create separate document libraries for different type of documents (teams/groups) to have different metadata / columns
Create separate content types for each team/group (inheriting document content type) >> add ...