Hi,

1) i think that you mean the chat component and not module... it's a component not a module...however i can't understand what is blank, if frontend or backend... contact me by email providing site address and admin account so that i can understand: This e-mail address is being protected from spam bots, you need JavaScript enabled to view it
2) Notifications for new messages are shown in the left column beside the user name in the page of the private messaging. If you want to give users a notification you can activate the email notification that works the same as Facebook.
3) If you mean the normal chatbox with the users list, this is not possible because it works with realtime logged in users also supporting guests users that are not logged in. For this purpouse has been developed the private messaging system.

Thanks,
best regards