Stealth 600 Gen 2 Black Wireless Gaming Headset for Xbox One
Xbox Series X
Yes. Any Xbox One model and Series X|S as well.
No, they are made for small heads and there non adjustable. Do not buy this brand it's the most uncomfortable headset. You Will Be Sorry!!
No this one is only for the console itself. If you are looking for one that is both for your console and phone I would recommend the stealth 700 gen 2.
According to the product description, the Stealth 600 Gen 2 headset features "Xbox Wireless direct-to-console technology", meaning that it connects directly to the console and does not come with a wireless adapter for operation.
No there are ones for PlayStation
Yes they all should have one from what I am reading
Yes, via an Xbox Wireless Adapter. Xbox Wireless is a Microsoft technology that reduces latency, and is what this headset and Xbox Series/One controllers run on.