Upside? I'm not sure there is an upside to wireless headphones other than just not having a wire on the floor or something. I never use them. Technically, wireless means more electronics. More electronics means more stuff that can leak noise into the audio signal or interfere in some way with something else in the room. All your wires should be shielded but still....
I can't recommend any wireless headphones but I strongly recommend Sony MDR-7506's. They're proven, won award after award for performance and used by a lot of the top engineers in the business.
A receiver does what it's name suggests, it receives signals from whatever source you plug into it. If you have a home stereo then you probably have a component that lets you select between listening to your cd player, radio, cassette players, vhs or dvd input, whatever... That's a receiver.
