Adding one more point.
I just scanned API. I do not see any thing like user.getGroupName() or user.getGroups()
I would like to directly retrive name of group(s) associated to a user
Also any help in getting list of available objects will be good.
As for retrieving groups related to a user you will want to check out the GroupManager class. You can retrieve a reference to this class via the jiveContext.
Most objects in freemark are retrieved through webwork via beans, in this case the user bean is retrieved from the JiveActionSupport class. If you look at that class you will see both setUser and getUser. When you call this out in freemarker using ognl syntax, $The specified item was not found., what this does is search through all the beans in your stack and look for a "getUser" method.
When you see something like ?exists that is a freemarker check for null, it returns a true or a false so generally is contained within a freemarker if block. More information can be found on freemarker here:
There are a lot of things in the context that you have access to. WebWork gives you the action, but we also add other things that are commonly used throughout the application you can find these defined in JiveFreemarkerManager class.
Hope that helps,