Distributing published papers if I am the first author
Different publishers have different guidelines, but I think they all allow your first case. For example, Elsevier's author rights page states:


  Authors transfer copyright to the publisher as part of a journal publishing agreement, but have the right to:
  
  
  Share their article for Personal Use, Internal Institutional Use and Scholarly Sharing purposes, with a DOI link to the version of record on ScienceDirect (and with the Creative Commons CC-BY-NC- ND license for author manuscript versions)
  ...
  


If you're worried, I do recommend checking each publisher's page to verify your rights.