HAL has singers, instrumentalists, comedians, dance ensembles, magicians, and a few other miscellaneous type entertainment, not big production shows. However, HAL does emphasize the great itineraries much more than other cruise lines. Ask yourself if the entertainment is your goal or seeing ports and scenery.
I think they have trivia every day ... and often more than once a day. We don't attend, but it seems to be listed constantly on the daily program.
Can't answer the other 2 questions at all.
We were on the Oosterdam last fall for 4 weeks. Had a great time. Enjoy your cruise!!