There's a coffee bar at the site but that's about it - coffee, cold drinks, crisps etc. But, as others have said, you're a 5 minute walk from the Old City (albeit up hill) where there's a vast array of places to eat. Try some local humous

Car ride should be 5 minutes. The walk is only 20 minutes from the hotel. There are tons of places to eat in the old

City which is steps away, and there is a good option at the park as well.

Yes. We paid 45 shekels. And yes there is a snack area (although I don't think pizza was an option) keep in mind you are minutes walk to the kotel where just above you have a large food court area.

I think you mean the Prima Kings hotel. That is close to the Old City. A cab ride should take about 10-15 minutes depending on how traffic is moving at that time of day. That ride should cost 50 shekels max that's about 12 dollars. Many cab drivers would rather be paid in shekels so consider changing money when you get to Israel. Also, you'll get a better deal if you pay in shekels. You can ask for a price when you get in the cab instead of just relying on the cab meter. There are more places to eat near your hotel than there are near the City of David, so I'd go get something to eat first near the hotel, say on King George Street, which is the street your hotel is on or at the Leonardo Plaza across the street (they have an excellent dairy restaurant there called Primavera) and then hop in your cab to go to the City of David. You can also get pizza, falafel, bagels or bbq food inside the Old City if you prefer to eat nearer to the City of David as the City of David is across the street from the Old City.