This http://www.knoppix.net/wiki/HD_Insta...g_not_to_do_it Wiki entry explains why you have problems that include (but are not only) installing programs to a Knoppix HD Install, and why it is better to install Debian.
You will find information about Debian and how to use it here
http://www.debian.org/doc/manuals/debian-faq/

BTW Debian now have their own 'variant' of Firefox called Iceweasel for trademark reasons, however if you want to use Mozilla's Firefox binary for Linux that loads perfectly well in Debian (but not as a Debian Package).
For example, download the firefox-2.0.0.8.tar.gz tarball to your working directory, and with root privilege
Code:
tar zfvx firefox-2.0.0.8.tar.gz --directory=/opt
(or whatever target directory you want), then create a KDE menu button with path to execute /opt/firefox/firefox

If you already have plugins installed you may need to symbolically link to them from /opt/firefox/plugins