Can firefox be installed on Debian Lenny 64? Will this cause problems with dependencies? How can I install it? I want to get some of the extension I like using in my browser. Iceweasel version is too old for some of the Add-Ons.

There is nothing to install. This is how I use Firefox:
download Firefox
extract to my /home
ln -s /usr/lib/iceweasel/plugins /home/craig/Downloads/firefox/plugins
opened iceweasel with iceweasel -profilemanager and created a profile for Firefox
copied my iceweasel profile to the new firefox profile

created a Firefox.desktop so I can launch it by clicking on the desktop icon.
[Desktop Entry]
Encoding=UTF-8
Version=1.0
Type=Application
Terminal=false
Name[en_US]=Firefox
Exec=/home/craig/Downloads/firefox/firefox %u
Icon=/home/craig/Downloads/firefox/icons/mozicon50.xpm
StartupNotify=true
Categories=Network;WebBrowser;
MimeType=text/html;text/xml;application/xhtml+xml;application/xml;application/vnd.mozilla.xul+xml;application/rss+xml;application/rdf+xml;image/gif;image/jpeg;image/png;

Although the last time I checked Mozilla did not have a 64bit version of Firefox. You might try using Swiftfox instead.

I ended up doing this:

Fisrt adding backports to the /etc/apt/sources.list

then,

There is no firefox for a 64-bit system - you need to compile it from the sources.

The Firefox nightlies have a 64bit version, or you can download it from the Mepis repos.

http://main.mepis-deb.org/mepiscr/re...epo1_amd64.deb

Of course Iceweasel has a amd64 version as well.