If you want to install Firefox systemwide, so it can be used by all users, you have to do everything as root. Install it for example in /usr/lib/firefox .
If you install it from your user account you can install it only in your home directory and you are the only user that can run it.
Don't have to install it twice, user and root, best it is to do it as root.
Go and install it in an other directory, then remove the one you installed from.
Uuups, someone was faster than me