This same issue happened when i was developing with my localhost using xampp (offline) so i dont think its a server issue.
I think its a plugin issue. I removed the last plugin i installed (just deactivating) didnt fix. WHen i deleted the plugin it my icons came back!!
The plugin that caused the issue on localhost was something else because i just used a new plugin.
The funny thing was that after i installed the plugin things were still ok, after a while it went strange.
So i definately think your theme has issues with various plugin compatibility. Looks like maybe other add-ons that have some font awsesome function override your settings. Really odd!
The offending plugin was “Bootstrap 3 shortcodes”. But you will have to play around for a few hours before things go funny after installing it.