Don't use the app for booking dining ahead of time. I assume you are doing my time Dining, go ahead to https://www.royalcaribbean.com/ and make your dining reservations online using the Cruise Planner. As far as entertainment, if the Independence OTS has pre-reserved shows, you'll be able to do that also. But I'm not sure the Independence has prereserved shows. I think it's only the Oasis Class ships and the Quantum class ships.
The app works great when you check in and when you are on board but not ahead of time for dining. The cruise planner is what you want to use ahead o