I believe it's possible to run 2 versions of Firefox on the same system if one of them is a portable version. Mozilla Firefox 6 Portable Edition.
Though as far as I know, the problem with FF6 and Java is only with the Java Console Plug-in. This shouldn't affect the average user though and Java should work just fine in FF6. More importantly FF6 contains security fixes, so you should update soon for that reason alone.
It looks like you may also be running a very old version of Java. Please visit THIS SITE
to verify you have the latest version installed. The latest secure Version is jre-6 Update 27
. Be sure to uninstall all old versions of Java before installing the latest.
It is especially important for your systems security to keep Apps such as Java, Flash and PDF viewers up to date, as outdated versions of these Apps are among the most popular vectors of attack for malware.
A good way to keep informed if you have the latest updates for these and other popular Apps, as well as the latest MS security updates installed, is to use Secunia's Online Software Inspector