Re: Shadowing a Writers Room
This happened to me before I got my first staffing job. My advice is just listen, the showrunner might actually ask you what you think about a pitch of if you have any ideas. If you do, feel free to pitch. If you don't just mention how much you respond to one of the ideas that's already being considered and state why.
Ask the other writers questions but not during room time. Ask before room time starts or if you're in a room that has an actual lunch break ask questions then.
Most importantly treat this as a learning opportunity for you to grow as a writer and not an opportunity to staff. Also be kind and gracious to everyone down to the writers PA.