My wife and I are both in our 70's and she's mobility challenged. The ship (the Serenade) was very accommodating to her as they had wheelchairs and golf carts available:
1. The Intercontinental on St. Charles Street. We didn't stay there because NO was the end of our cruise and we'd already booked the Wyndham, in the French Quarter, so I can't answer your questions about restaurants close to the hotel. We ate in two excellent restaurants, Tujague and Antoine's, which were very close to our hotel and a short cab ride from the Intercontinental. Tujague had the best food I'd ever eaten.
2. We went on an excellent three hour city tour as an excursion from the ship. It ended at the Intercontinental so I assume it begins there as well.
3. Coke products. I'm not sure about the coffee drinks available other than decaf, which I drank at every meal.