Applet, to have communications it needs to be signed. This is not too difficult though.
applet don't have to be signed if they want to communicate with the server they are hosted on, and now they also have cross domain support, so no longer need to be signed to connect with any server.http://weblogs.java.net/blog/joshy/archive/2008/05/java_doodle_cro.html
Applet to go fullscreen however will need some tricks, like popping a JWindow to get out of the browser window. I had trouble getting that to be stable when 'undecorated', and still haven't had time to figure it out.
not if you use a lwjgl applet or a library like slick
they have proper fullscreen support.
example of slick applet with fullscreen support here