Is it possible to share an HttpSession between a JSP and EJB? What happens when I change a value in the HttpSession from inside an EJB?

You can pass the HttpSession as parameter to an EJB method, only if all objects in session are serializable. This has to be consider as "passed-by-value", that means that it's read-only in the EJB.
If anything is altered from inside the EJB, it won't be reflected back to the HttpSession of the Servlet Container.The "pass-byreference" can be used between EJBs Remote Interfaces, as they are remote references.
While it IS possible to pass an HttpSession as a parameter to an EJB object, it is considered to be "bad practice" in terms of object oriented design. This is because you are creating an unnecessary coupling between back-end objects (ejbs) and front-end objects (HttpSession). Create a higher-level of abstraction for your ejb's api. Rather than passing the whole, fat, HttpSession (which carries with it a bunch of http semantics), create a class that acts as a value object (or structure) that holds all the data you need to pass back and forth between front-end/back-end.
Consider the case where your ejb needs to support a non-http-based client. This higher level of abstraction will be flexible enough to support it.