The left side bar rearrangement, showing only one class at a time, really hampers usability for anyone in more than one class, but especially for more than 2.
I have to go through the classes to find which has the notification, and then finally see whether it is a new question, or just TAs chatting. It is annoying, especially since there is plenty of real estate.
Since your class icons are circular, you have 4 corners that could be used both for notifications and for menu selection -- more of a dashboard of class status, with an interaction that works on both computers and mobile devices if you can use pop-up circular menus. I'll quickly learn whether a notification number in the corners mean chat or question or other if a circular menu pops up (Feed, Rooms, Settings) when I hover over the class image.