I found a way to get embedding youtube videos to work. It’s a bit of a hack but a very simple one. In the fep-class.php file if you comment out lines 308 & 309 embedding works fine:
//if (!$message['message_content'])
// $errors->add('invalidMgs', __('You must enter some message content!', 'fep'));
Without commenting out those 2 lines, the youtube embed code never makes it into the database.
I can confirm that I having the exact same problem. Does this require paid support?