You should be able to change the settings of your stream to only include things you want to see.
If you are not interested in replies, just click off the Follow Discussion button, which will be green if you are following. Is this what you mean? I am not sure if you can disable announcements on your progress, etc.
Yeah I am more interested in disabling announcements on my progress so I can see more easily discussions that I want to follow.
conversely, I don't want to follow every discussion I've posted to . . . but duolingo automatically signs me up to follow . . . I'd like to be able to customize that without having to go back and click "unfollow" for every one.