What is the ruling on a worshipper kneeling to supplicate after each obligatory prayer, and then wiping his face thereafter?

Supplicating (Du'a) after the prayer is legislated, but it is better not to commit to it after every obligatory prayer. The reported remembrances (dhikr) should be given precedence. There is no specific sitting posture for du'a; it is valid however one sits. It is not appropriate to designate a particular sitting posture for it. As for wiping the face with the hands after du'a, there is a difference of opinion regarding it.