Do the Koss PRO4S need a headphone amp?

No. At 35 ohms and 99 dB sensitivity they play loud enough from a phone, laptop or mixer output. A dedicated amp adds headroom but is not required.

Can I plug the cable into either earcup?

Yes. The PRO4S has dual-entry jacks, so the detachable cable connects to the left or right cup. That helps when routing the cord around a desk or mixer.

Do they have a microphone or remote?

No. There is no built-in or in-line microphone and no remote control. They are for listening and monitoring only.

How well do they block noise?

Isolation is passive only, through the over-ear pads. They soften some room noise but will not silence a loud office or commute like active noise cancellation would.

What comes in the box?

You get the headphones, a detachable coiled cable and a 6.3 mm adapter for studio gear. The cups fold for storage.

Are they good for studio mixing?

They suit home mixing and monitoring with a balanced, wide-range sound and a 6.3 mm adapter for interfaces. For critical mastering, many engineers still prefer open-back or calibrated reference models.