1. Did you clear cache after changing setup?
If you want to send message only to admin you can set your admins in Dashboard > Front End PM > Settings > Recipients and set 0 in “Max Recipients” field. It will remove the ability to send message user to user.
2. If user subscriber delete any message, that message does not get deleted from database. You can still see that message. You can also reply that message if you want and that user also get that reply. Go to Dashboard > Front End PM > Settings > Security and check “Can user reply messages deleted by other user?”
3. This plugin uses default wordpress options to show any media. If you want to show beyond that there is a easy hook to do that. Please use
fep_filter_attachment_download_link hook to change that link to show directly the media instead of downloading. As this require custom code, if you need my assistance you can contact me through https://www.shamimsplugins.com/hire/
5. message inbox/sent is determined my last sender of that message. So if someone else is last sender then that message will end up in your inbox and vice versa.
Let me know.