Several things: I use Gome shell in debian stable with firefox 21 and it works perfectly. Are you behind a proxy?.
If you are not, you have several options:
First: Make sure you have the plugin enabled (just write about:plugins in the navigation bar and press enter). If it is not, just upgrade gnome shell.
Second: Check you have installed the extensions in /usr/local/gnome-shell/extensions . If so, copy them and paste in /home/YOUR USER NAME/ .local/gnome-shell/extensions. You can also manually download the extensions from the developer web page, and copy in this folder.
Third: You can try and use Chromium to istall the extensions (you should enable the plugin by typing about:plugins in the naviation bar)
Fourth: Reset Gnome: here
you can see how to do it in Ubuntu , in LMDE should be the same. You can also try to purge Gnome and reinstall it again
FYI, Caja is not Gnome is MATE. You don't have to use GNOME 3 or its extensions, if you like the old GNOME 2, you can always use MATE or SOLUSOS. The best thing about Linux is that if you don't like one thing you can always find an alternative