1. and 4. is possible.
(So long as they don't use third party software).
can't prevent from saving?
No. Consider: what would happen if there was no PDF viewer at all in the browser or system. User would get a prompt to save an unrecognised file, whatever protection there was.
I think maybe you want DRM.
Hi, what is the DRM?
I want to protect PDF that are stored on SharePoint.
DRM - Digital Rights Management. Controversial area.
DRM does not stop files from being saved, copied etc. as this is impossible. Instead if focusses on controlling who can open and read PDF files.
Adobe's enterprise-level product is LiveCycle Rights Management, which needs to be part of an enterprise level document security strategy agreed at the highest level; it can also manage some Office documents. The consequences need to be fully understood especially with regard to non-Adobe viewers and that it mostly makes viewing in browsers impossible.
Or, some large publishers use LiveCycle Rights Management, to secure ebooks.