Yep, cookies are per domain, not even per sub-domain :)
We do not have such feature for security reasons - we do not want someone to ping a site and start asking if users are logged in. You can do a small web service tough in the Sitefinity site pass parameters like user/e-mail and it should return true/false if the user is online. Or, the web service can just have..
IList<User> users= SecurityManager.GetLoggedInBackendUsers()
.. and you'll have all online users at once.
I believe, these articles will be helpful.