You've mentioned that after fully washing the arm, new moisture should not be acquired. My question is, when washing the arm sometimes water goes on the sleeve as well, and while wiping down the arm – particularly above the elbow – to ensure all areas are covered, the palm of the hand may touch the wet sleeve once or more than once. Is this considered as acquiring new moisture? Should we try to avoid our hand touching the sleeve?

Your hand touching the wet sleeve is ok. It doesn’t invalidate your wudhu