Indeed. Luke has failed Yoda twice already (the cave, Bespin) but he doesn’t want to take his father’s path. Luke has changed… and his father begins to change as well (does he kill Piett at the end like he “should” do it ? No, he just walks away).
Did he go back to Yoda after that? No, he failed Yoda again by deciding to go on another “friend-saving” adventure just at the end of ESB.
Regarding Piett, it is my speculation against yours, but I think at that point Vader was in a different world and just did not care about such a petty thing. I doubt he spared him because he suddenly became a “better person”.