Can you check your Chrome version? Soothsayers who turned on Chrome notifications with an older version have been experiencing the problem. We upped the requirement to Chrome 50, so this problem shouldn't happen for beta testers, but might occur for soothsayers. "New activity has occurred" also happens if you're logged out, I think. If you could send a screenshot of your console while this happens, we can figure out what's going on.
In terms of stacking, we update an existing notification with the new notification if it's the same type. I think that's useful for chat messages, but maybe not as useful for friend requests / new followers. We can look into stacking differently.