glut fullscreen problems: xinerama, mouse and focus

Using glut I have written a program that works fine in windowed mode, however in fullscreen mode, there are a few problems:

How do I hide the mouse?

glutFullScreen takes over all monitors, not just the current one. I would like fullscreen to use just one monitor. How can I test for this and have it be portable in windows and linux? If one monitor doesn’t support opengl, how do I test for this?

When I return to windowed mode by calling:
how do I give the window focus? The focus changes to another window. Is this wm specific?