1. Maybe, but you can certainly call and make reservations from your cabin as well as appearing in the dining area itself.
3. Yes, they are the same show but set up at times so that those dining early seating can attend one and those dining the late seating can attend the other. You have enough time after dining to attend. In addition, there will be a few 'midnight' adult shows.
4. Yes. This ship has in-cabin booking AFAIK. You can also go immediately to the shore excursions counter and place your bookings there. They will be open from the time you get on until late that evening.