.gnome2/ contains configuration files for applications, much like .config/. However .config/ is standards compatible (FreeDesktop). While .gnome2/ exists to be used by the now depreciated gnome-config. .gnome2_private/ is like .gnome2/, but for configuration files that need to be private.
gconf.xml.mandatory and gconf.xml.defaults are XML for desktop settings like your local .gconf. gconf uses all three to configure the desktop. .mandatory can not be edited by a normal user, making it useful for kiosks and public-use computers, while .defaults is the base from which all default desktop settings are read.
In order of priority, .mandatory comes above (your local) .gconf, which in turn comes above .defaults. If a key is set in .mandatory, the same key in .gconf and .defaults will be ignored. Likewise, a key not set in .mandatory but set in .gconf, will override the same key in .defaults.
This is also the case for .path.mandatory and .path.defaults - except they are used to set the location of configuration sources, rather than describing the configuration itself.