We have set the application 'Discuss' with all the 'Stream' options on and also set them all on in the EasyDiscuss integrations settings under 'Activity Stream', yet nothing is appearing in the stream when things happen in EasyDiscuss?
Also in testing I found that when the user logs back in and goes to the discussion page, it's not showing a notification icon there that there is a reply.If you enter that discussion page, the notification will be considered 'read', but it will still be in the notification list(http://take.ms/dNjJU).
It would seem logical that if someone posted a reply to something you wrote, you would see that even if not friends with themCurrently I believe system notifications in EasySocial will notify the discussion owner as well, provided the integration is enabled. Perhaps you create a feature request for this to suggest a better way to integrate this with the 'Everyone' filter disabled.
Checking as per your image, it did partly show in that it showed someone had replied but not that there was also a comment.I have tested comments and it appears to be generate correctly as well(http://take.ms/mevD2).
Currently I believe system notifications in EasySocial will notify the discussion owner as well, provided the integration is enabled
On the other hand, site admins should be able to view all user's discussion stream items in the dashboard's app filter(http://take.ms/iPzVP).