You mention inline tagging of people. I guess then that there will be a notification API built into CB no?
You don't tag people. You mention them using @USERNAME, @NAME, or @USER_ID. It's the same usage as Twitter basically. Currently when mentioned the activity will not show up on your personal stream, but it will in either RC2 or a future release.
You mention #Hashtagging. How does this work?
They filter down activity to show all activity with that hashtag in it. Same as Twitter, Facebook, and other social sites basically.
Will GroupJive have the same comment features enabled? Because this comment feature and the inline tagging is what would be most useful, more useful actually then CB activity update (although it is interesting the stuff you have updated).
In its upgrade, no. In its complete rewrite, yes. In the rewrite GJ will barely do anything without CB Activity. CB Activity provides an entire streaming API. An activity stream can be generated for anything. The GJ rewrite will use that API to have a per-group stream. The rewrite however won't be until after the upgrade release to improve compatibility.
Will Kunena integration into CB activity still work? What about GJ integration into CB activity?
CB Activity does not track activity. Other plugins, extensions, etc.. will log activity using CB Activity API. So for example CB Auto Actions could be used for thousands of activity scenarios. CB Blogs and other core plugins will also be updated to log their own activity and handle their own activities displays.