Heh... good questions :-)
I don't know (maybe some more embedded oriented guys can help you more).
But I would just try - try calling hide() and show() on the desktop widget and see if it does what you want. (please post back what the result was, it would be nice to know! )
Same for second question - you can sure call resize() since it is a QWidget, but the rules for hiding, showing and resizing may differ for it, and be controller by qws.

Another solution would be to access the video buffer directly and render it in a paintEvent() (if you can!), or similar, but I expect that to be not trivial.