Using Awasu Advanced Edition 2.0.5 beta, although these minor bugs have been present since at least 2.0.
I run Awasu from the system tray, and normally keep the window maximized whenever it is in use. Otherwise, the window is closed/minimized to the systray. The item pane is not set to be automatically hidden.
1. Sometimes clicking on an item in the item pane causes the Awasu window to be restored (i.e. un-maximized). I've not been able to distinguish any sort of pattern as to why or when this happens, I'm afraid.
2. On opening the Awasu window from the system tray, the control center is 0 pixels wide and I have to drag it back to proper width. This only happens when synchronization (either save or load) has been triggered externally while the Awasu window is in the system tray, so I doubt it's affecting many users.