The cable is fixed and max. 1.20m long. As mentioned, the plug goes into the green connector on the front or on the back of the main board or sound card.

No, cables are fixed.

The small jack plug is normally connected to the green connector. (Front) This connection is available on every desktop PC. I don't know whether the small cable was included in the delivery. It's probably part of the scope of delivery and unfortunately it's not clear from this. Have a look at Logitec, the scope of delivery is certainly described there. (The cable is certainly included, it costs the manufacturer almost nothing).