I am left-handed. On the top bar, I need the System menu (and Logout, User Switch, Clock, Battery Status, etc) on the left side. And I need the global menu items as well as the window buttons (close, minmize, maximize) on the right side. How can I do this?
You can't do that. I remember reading some thoughts about doing things like that (I think with regards to right-to-left readers), but it hasn't been implemented yet.
Well. You can't do that with the Unity panel, anyway. I think it should be possible to replace the Unity 2D panel with a Gnome Panel, add the indicator-applet-complete and the global menu applet, move the window buttons and achieve the same effect that way. I haven't tried it myself, though, but it should work. It would require some tweaking.