If I recall correctly, @Pginer-WMF's designs called for "mark as read" to be an option in the dotdotdot menu, but right now it doesn't appear there.
Regarding the icons:
- For mark as read: we are using the "check" icon, a tick mark to indicate completion.
- For mark as unread we are using the "sun" icon, basically a bright spot to indicate the notification is new again: