"Fallback mode" is just another name for "Gnome Classic"
If your graphics card is unable to handle the more demanding requirements of Gnome 3, or if you just prefer the "old school" interface you can use the fallback instead.
If you've installed gnome-shell, you should have both Gnome Classic (Fallback) and Gnome 3 available at login.
I apologize for being unable to help you as much as I'd like. If you'd give me more information regarding your issue, I'd be glad to help?
As far as your problems with installing fglrx, I can't help you there. Hopefully someone else can get you on the right track though. :)