A:AnswerYes it comes with a propriety cord which is 2.5 mm in one end. Unfortunately, that means you can't use any AUX cable, and have to rely on Senheisser's cables, which tend to be pricier, but it does come with one cable.
A:AnswerYep, but if you choose to use the microphone as well then the connection bandwidth is very limited and the audio quality drops significantly. The only headsets that avoid his problem use a separate usb dongle and not bluetooth. I even tried using an aptx dongle on my ps4 and still microphone was a no-go. I got the PlayStation platinum headset and it works like you’d expect with high quality audio and microphone at the same time.
A:AnswerYou cannot use the optical out. But I would bet there is a mini jack sound out connection. You can use the cable supplied with these headphones and plug them into that port and they will probably work fine. You may need to buy an headphone mini jack extension cable depending on how close you are to the TV. The extension cable would need to be female jack on one end and male jack on the other.