Are there many shops/restaurants within walking distance?
No, you have to take a cab, Uber or any transport. They are too expensive, I recommend you ask first the cost to the driver.
No I'm afraid not. It's a good walk to any decent shop or restaurant. Although central Nice has everything and is one stop on the train.
I do not believe so.
Get an answer from Novotel Suites Nice Aeroport staff and past guests.