Install firefox to /usr/share/firefox
Place a link to firefox.sh in /usr/bin
ln -s /usr/share/firefox/firefox /usr/bin/firefox
Start X and open a terminal window.
If everything is installed properly, this should solve the problem.
Normaly there should be no need to change any permissions.
But there has been an issue that there might be problems when Mozilla and Firefox are installed in the same directory.
I donīt know if this still is the case, but I had problems before when I had Firefox and Mozilla both installed in /usr/share
They both were not able to open any websites, as if there was no connection to the internet.
Also you should start firefox the first time as root. ( Only start it one time ! Do not use it as root ! )