No, this is just an overnight stay hotel with a very basic (!) breakfast. So better eat at the airport or buy your snacks at the airport before taking the shuttle
Not in walking distance. If you have a car, there are restaurants in the area. I can't vouch as to their quality since we did not go to any. We ordered pizza and sandwiches from a place listed on a card in our room. The desk clerk took money from me and paid the delivery and then brought the food up to our room! What a wonderful service.
There is absolutely nothing around except a burger king
Get an answer from Best Western JFK Airport Hotel staff and past guests.