Here's what I did:
% tar xvfz firefox-1.0PR-i686-linux-gtk2+xft-installer.tar.gz
This creates the firefox-installer directory. The installation itself was done as root...
% su -
# cd /home/gavollink/firefox-installer/
# ./firefox-installer
This brings up a GUI installer ... I installed to /usr/local/firefox.

See above the permissions tweak that I had to do to get it to run as a user.

Now the cool thing (I'm using Gnome on Fedora Core 2 - your results may vary)... the first time I ran Firefox as a user, it asks if you want to set Firefox as your default browser. If you say yes, then the redhat-web icon on the menu/toolbar will launch firefox.

Good luck.

I heard somewhere that you have to run it as root first, then as a user.

For the gmail problem, I press Ctrl then click on the links. It works fine then ;) [I mean, everytime I open something, like composing a mail, I have to press Ctrl]