Which PDF reader that can save current sessions of multiple files from different folders, so that when I reopen it the sessions are restored?
You could try Foxit reader (This guide is for Windows). I occasionally use a portable version, and has a feature for saving and restoring session with multiple tabs irrespective of source folder.
You can configure like so:
Foxit Reader -> go to "File"->Preferences -> History >tick Restore last session when application starts and see if this option is what you're looking for
Additionally you can have multiple pdf files opened with a tabbed view, see below:
More information please check here: https://www.foxitsoftware.com/products/pdf-reader/
Best I can tell Skim meets your requirements. In the Skim preferences, there is a checkbox to open files that were open during my last session. When I check that box, Skim opens 2 files from 2 folders that I was working on.
Both Firefox and Chrome (don't have MS products to test with) let me drag-n-drop a PDF file from my local file system into a window and they render the file fine. Multiple tabs worth. Bookmark the group of tabs.
PDF-XChange Viewer can do this, and is better than Nitro or Foxit. The latter are heavier, slower, non-free and don't have any better feature comparing to PDF-XChange Viewer.
It has a Restore Last Session button:
and save recent documents: