I think Lix also does mouse capturing which may have some role to play in causing some of the symptoms (eg. maybe that's why clicking on the application icons on the taskbar didn't seem to work, if the input is still being captured and directed to the Lix window), though I thought in Windows it's supposed to release the capture once you switch away to another application. Unless it doesn't count yet when you bring up the Taskbar via the WIN key?
The capture only seems partly removed when pressing the Win key:
a) You get a duplication of cursor: the Lix crosshair and the normal Win cursor,
but if you move the (Win) cursor, both move simultaneously (at least when on the Lix "plane").
b) It is actually quite hard to click on the Taskbar without refocussing Lix.
c) Clicking on the Taskbar seems to reunite the cursors for (at least) when not over the Taskbar but over the Lix "plane".
(That's actually quite similiar in windowed mode (apart from b) generally) though there it is nevertheless a way to effectively free the mouse.)
Edit:
- The shortcut Win+m ("Minimize all windows") brings the Taskbar and lets you produce overlapping windows by clicking on the tabs (but Lix remains on background/doesn't minimize).
- The shortcut Win+d ("Show desktop") gets you to the Desktop but if you open another window Lix gets on the background again. (Basically the same as with Alt+Tab and choosing Desktop.)