Supinator is the only muscle to insert within the forearm, and the only muscle to act upon it.
Each of the "pollicis" muscles (abductor pollicis longus, extensor pollicis brevis, and extensor pollicis longus) each act on the thumb and on the hand, because they cross both the wrist and the joints of digit 1 within the hand.
Extensor indicis is the only muscle to act on digit 2.
The deep muscles of the posterior forearm are innervated by the radial nerve.