You can think of it just as the price. Availabile means whether or not they have rooms. Reservation is to buy a head of time to make sure you have a room. Rate refers to how much it costs per night.
So I imagine a hotel would say: Please look at our available reserveration rates below... and then list the prices. You could ask: What are your available reservations rates? But, I would just say: How much is it for one night?