RE: Why doesn’t Ben kill a defeated Vader?
Jedi Knights are honourable and chivalrous. Killing an opponent in a duel is one thing, but killing a vanquished fallen opponent is something entirely different. That is an execution.
We already see that when Anakin ‘executes’ a defeated Count Dooku. It is a wholly evil thing, and not the Jedi way.
So leaving Vader alive to murder millions of people is honourable and chivalrous? The situation with Dooku is not comparable, because Anakin had the option of letting Dooku stand trial. Obi-Wan on the other hand has to choose between two evils, where letting Vader live is clearly the worse option. Also, Yoda in ROTS sends Obi-Wan to kill Anakin, and Obi-Wan tells Luke, that if he will not kill Vader, the Emperor has already won.