Index papers by the documents in which I mentioned them

  1. in each paper’s details add the google docs documents in which I used it as a reference.
  2. on the sidebar - add the option to present all papers within a document.

Your # 2 request is possible with the Google Docs add-in:

https://chrome.google.com/webstore/detail/paperpile/imanmdcibgaflfaibbcmmkifdgllfopm