All judging sessions are closed. Team members, only, as well as one to two coaches, and one historian. I always have my kids introduce themselves to the judges as they walk in...they had to walk in anyway, and it makes the judges less intimidating to the kids.
You won't need a poster for Core Values, but perhaps in project. Core Values judging is an activity that the kids will participate in; so I wouldn't worry much about that one, except to make sure the kids are in tune with each other, and know how to show each other gracious professionalism. This one is more about how well they work together.
Kids should know their roles in judging sessions. Judges usually ask questions of all the kids; however, they usually ask more build questions of the obvious builders. It is always OK for a team member to tell the judges that a specific questions was not in their area of focus and refer them to another team member. They shouldn't answer EVERY question that way, however.
Mission judging occurs on the table during the robot competition; it's how scoring is done. There is no separate judging session for that. It is wide open for all the world to see! Two and a half minute on the table for three official runs (and one practice run); scoring is the best out of the three. Practice tables are first-come first-served. Some tournaments have signup sheets. Get to the tables early to make sure you have a spot, because you won't get long on the tables!