Which extra libraries do I need to deploy for my applet to work with the components from JBuilder - "DataExpress" and "DB Swing" ?

The DataExpress and dbSwing classes from JBuilder are of course, not part of the standard Java VM. So additional classes need to be deployed. The file /jbuilder/redist/deploy.txt lists the files that you are allowed to redistribute from JBuilder.

In particular, in JBuilder 3.5 the files that you require are located inside dbswing3.1.jar and jbcl3.1.jar