I realize that we are supposed to be at Java 8 Update 76 or above, But I would like to know what parts of Windchill still use Java and what happens if the Java version isn't at Java 8 Update 76.
Windchill is one giant Java application. The whole thing is using Java. It is certified with certain updates of Java but that doesn't mean it won't work with other updates, but you will probably be on your own if you run into issues. Keep in mind as well that Windchill comes bundled with it's own version of Java and, unless you tell it otherwise, it will use it's own bundled version exclusively and ignore anything else that might be installed on the system.
That's exactly what I'm looking for, Would be nice just to have to worry about Java versions on user PC's.
Ah, in that case you want to read this article: https://support.ptc.com/appserver/cs/view/solution.jsp?n=CS160578. It lists every place that a Java applet is still used.
Just a point of clarification:
Use of Java applets in web UI's, however, is a completely different beast -- requiring the Java Plugin or Java Web Start (which are both part of the JRE) for JNLP-launched Java applications and adding a lot of complexity, fragility, etc.
And server-side Java is, of course, another matter entirely -- and there a JDK can be installed just for the server application in question and it does not have to interact with web browser(s).