the plates are probably adapters. You get cleats with the pedals.

first, what shoes did you buy? Can you return 'em if you decide you want something else? What are your short and medium term goals/plans? Are you looking to do long, say, 3 hour rides or are you happy with less than two hours? Do you have any knee issues?

ebay... you're probably looking at used pedals, which means the cleats are probably still being used by the seller or they were simply too beat up to sell with the pedal.