I am not saying I can do it. But I can try.
Need to know the notification stuff. The alerts normally have class .pm_indicator, .likes_indicator . Which functions send the no. of mentions for message and mentions ? Which function should I call to get these numbers ?
Ok, here you go :)
With sidebar menu and refresh button ;)
(http://www.elkarte.net/community/index.php?action=dlattach;topic=3013.0;attach=2977;image)
Honestly, if I were to write an app I would write an addon for elk as well to expose the stuff via json (a thing that I started a while ago, but never finished), so that it would be much easier to grab from the app what is needed without having to parse the html to find classes, etc.