Is there some way I can track all applications that were opened by a user during a gnome session in ubuntu?
Do gdm/gtkwm keep a history of all applications that were opened in some log file?
Take a look a the Gnome Activity Journal. I've only read about it, but it might have something you could use in there.
No, to my best knowledge there is no way to do this within the desktop or window manager.
But take a look at gnome deployment guide for some lockdown options. Maybe one of the kiosk mode options is of some help.
It might be easier to convince apparmor or SELinux to provide such a log.