Is it valid for one to perform the Sunnah prayer while sitting, from the takbir to the taslim, with the ability to stand, indicating bowing and prostration with gestures, and is it considered a valid prayer?

There is no objection to performing the Sunnah and supererogatory (nafl) prayers while sitting, even if one is able to stand. It is permissible to begin the prayer standing and then sit, or to begin it sitting and complete it likewise. The reward for one who prays sitting is half the reward of one who prays standing, unless there is a valid excuse. One who prays sitting should nod for the bowing (ruku'), and it is preferable to prostrate on the ground and not merely nod for prostration (sujud); however, if one nods for it, their prayer is valid.