hello Christian Mayrhofer,
Sorry for late reply to this,
I have checked and tried to uploaded avatar image in your profile, it seems like the system unable to create a new folder when the user trying to upload the first image in your site, because the system need to create a new folder for the userid folder for store different user image file. check my screenshot below.
Not Found
The requested URL /media/com_easysocial/photos/6/15/32255-121697754525998-128355057212158-221995-4545734-n-jpg_large.png was not found on this server.
By the way, i also noticed that your file permission get denied when the system tried to access
...media/foundry/4.0/config/ce30db8db64f8c2aa7f45a1211146a10.js
Warning: file_put_contents(/xxx/xxx/xxx/xxxx/public_html/media/foundry/4.0/config/ce30db8db64f8c2aa7f45a1211146a10.js): failed to open stream: Permission denied in /usr/local/sites/gapalumni19HAw/public_html/libraries/joomla/filesystem/file.php on line 431
Can you consult with your Webhosting provider regarding this? and make sure the all the Easysocial folder/file is accessible and give system permission to create a new folder in your site. Keep us updated then when your webhosting provider responded.