A:AnswerYes the headset has a cord which is attached to a hub which is connected to PS4. I keep the hub on top of the PS4 console, so it's basically as though the headset is connected to the console. I think the cord is about 15 feet long.
A:AnswerNo the headset is wired. I'm glad about this because the cord is long enough for me (about 15 feet) and I don't want to worry about recharging.