The wirelessly enabled chairs have a wireless transmitter included as part of the package.  The wireless receiver is housed inside the chair itself.

This is not mains powered.  It requires 2 x AAA batteries (not included).

The chairs are designed to be connected to the TV/monitor using the audio out connections on the monitor and the audio in connections on the chair. Your console remains connected in exactly the same way it was prior to the introduction of the gaming chair into the environment.

Yes, all Sound Chairs come with Bluetooth connectivity which can be paired to work with other Bluetooth Devices ie smart phones, tablets, monitors with Bluetooth connectivity.