I've seen lots of examples of JavaFX in my reading, but every JavaFX app I've seen need to be launched in a separate window. The apps don't run within a web page.
Can JavaFX applications be run within a web page, just like we would expect a Flash app (or, for that matter, an applet) to run? Is there a reason why people aren't letting JavaFX apps run within their web pages?
Is there a particular bit of HTML code that needs to be used to get a JavaFX app to run Flash/applet-style?
Yep, just use run application as Java Applet. NetBeans will deploy all FX stuff correctly for all platforms including Java Applet.
Yes, just build a demo JavaFX application in NetBeans. I'd be surprised if they didn't provide you with some type of 'Hello World' test app. Then take a look at the HTML page it creates.
If you run into problems getting your JavaFX app to run on a webpage, take a look at this question. The short story is that you can't just copy jar files and copy and paste the appropriate HTML into your webpage. You need to include the JNLP file NetBeans creates, and you have to edit some of the NetBeansy stuff in the JNLP file.