I didn't quite understand what happened with Missy and the master... She "killed" him so that he would regenerate into her and he then "killed" her when she turned her back on him. He made it sound like that was the end for her as well. No regeneration would be possible due to the way he did it. If thats the case, when they were deliberating how to kill the doctor by dropping him off the roof a load of times didn't the master just zap him like he did Missy?
The Master wanted to kill the Doctor over and over, but was just trying to threaten him. Just killing him outright without any torture wouldn't have been any fun for the Master. He's a bit like the Joker with Batman. Without the Doctor, where would the Master find a worthy and fun opponent?