JavaFX 2.0 currently not supported on platforms other than Windows. JavaFX team is working on getting it to all the platforms. Not sure about the mobile devices though.
HTML5 video and audio tags do allow online streaming. Youtube has an HTML 5 powered trial site:
http://www.youtube.com/html5
JavaFX does support building application which can stream the content Live. Do check out
http://www.javafx.com for more samples and tutorials.
If you have any HTML 5 related queries, please use
HTML and Javascript forums.