The social login buttons are properly trying to load the relative link to the following file:
media/sourcecoast/images/provider/button_facebook.png
Which means, on your site, the following image is trying to be loaded:
https://www.generalworks.rs/media/sourcecoast/images/provider/button_facebook.png
That is returning a 404 error for me, which is why it's not showing on your site. If it worked before, but doesn't now, it means something strange happened when moving to SSL. Usually, your files shouldn't change for such an update, but it seems like they did. Can you check if that file above (and other files in the /media/sourcecoast/ folder exist? There are also Javascript files in there which are used in the admin area... if those are missing or aren't loading, that would explain the admin area issues as well.
I hope that helps narrow things down, but definitely let us know what you find.
Thanks,
Alex