Does anyone happen to know if it is possible to make wine completely take over the keyboard?
When I press CTRL+ALT+arrow the desktop starts to turn (Compiz ) even Wine is in full screen.
This is not a bug or design error in Wine. It's actually a design feature for the X desktop environment. If it's only a couple of keyboard shortcuts you want to use in Wine/games then you should edit the keyboard shortcuts for Compiz.
Or you could start up a second X server ("startx -- :2 &" from some virtual terminal) without any window manager.