I have configured 4 workspaces in gnome Classic without effects, and this seems to work.
When I log in with gnome classic with effects (compiz) I also see 4 workspaces in the panel but when I click on the second workspace just the background image is shown.
There seems no way out of this background only Workspace other then Ctrl-Alt-F1 and restarting the window manager.
Ubuntu – Workspace switching not working with 12.04 and Gnome classic with effects
gnome
Related Solutions
Taken from an OP's edit:
Google Chrome's Hangouts extension had its "Keep Hangouts on top of other windows" option switched on. So you'll have to forgo pinning the Hangouts chats to the notification panel to get focus working properly again.
For workspace switcher, you have Workspace Indicator extension https://extensions.gnome.org/extension/21/workspace-indicator/.
For the cube animation, sorry I don't find any, but at least you can use Workspace Grid extension: https://extensions.gnome.org/extension/484/workspace-grid.
For the CCSM, unfortunately, we cannot use it anymore in GNOME.
Best Answer
I initially had the same problem with workplace switching and only the background showing in Gnome classic, but the fix to Alt-Tab does not switch also fixed this - i.e. install compizconfig-settings-manager, and enable "application switcher".
Then if you wish to customize the arrangement of the workplaces from 2x2 to say 4x1, you can do that under Applications -> system tools -> preferences -> compizconfig settings manager -> general -> General options -> Desktop size -> horizontal virtual size = 4, vertical virtual size = 1.