Do not put $JAVA_HOME/lib/tools.jar and $JAVA_HOME/lib in your CLASSPATH. It's not necessary to have these in the classpath. Also, Java 6 automatically looks in the current directory for classes, so you don't need "." in the classpath.
Just remove the whole "export CLASSPATH..." line.
Are you running a 32-bit or a 64-bit version of Linux? To be able to run Java in your browser, you need to have a Java plug-in for your browser, but Sun only makes a 32-bit Java plug-in. If you're running 64-bit Firefox on 64-bit Linux, then you'll not be able to run Java in your browser.
Try asking your question on a forum about Fedora Linux, there are most likely more people there who know how to run Java on that OS.