Yes, you can do this by holding down the power button when switching on the headset until the voice says Bluetooth Pearing, then it should appear in the Bluetooth menu for selection.

That's not true. A USB C adapter for wireless is included. Bluetooth is also included. It's all in the instructions. I often connect to my mobile and laptop.

No, with an adapter from Apple Lightning to 3.5mm jack you can also connect via cable.