Yes, everything you listed is free. There also is a great sauna, steam room, and a large mineral jacuzzi in the exercise area that is free. The Cafe' Promenade on deck 5 has free coffee, cookies, Pizza, and sandwiches 24 hours a day.
All the shows are free, you can easily have a great time without spending money. If you drink you will spend a good amount of money. The navigator is an awesome ship...our favorite.