On Windows, if you close Graal it can stay in the task bar ... the same thing should be available for Mac. This works for applications like iTunes, Mail, etc so that you don't have to keep the window open.
On Graal, when you hit the X button, it should go to the dock (like most other applications do) and use CMD + Q to quit it, right click the dock and quit, or in go to Graal -> Quit in the top left.
AND
Graal should have PM notification on Mac. This could be done much the way it is on the Mail application. Graal could also "bounce" when you receive a new PM, like how iChat and other applications do when they need attention.
Imagine something like that on the Graal icon in the dock.