Did Saul and Samuel kill all the Amalekites?
And Saul smote the Amalekites from Havilah until thou comest to Shur, that is over against Egypt. And he took Agag the king of the Amalekites alive, and utterly destroyed all the people with the edge of the sword. ...
No, Agag's mother was left alive.
And Samuel said, As the sword hath made women childless, so shall thy mother be childless among women. 1 Samuel 15:33
No, David killed them all a few years later.
And David and his men went up, and invaded the Geshurites, and the Gezrites, and the Amalekites: for those nations were of old the inhabitants of the land, as thou goest to Shur, even unto the land of Egypt. And David smote the land, and left neither man nor woman alive, and took away the sheep, and the oxen, and the asses, and the camels, and the apparel, and returned, and came to Achish. 1 Samuel 27:8-9
And then David killed them all again, just to make sure. (Except this time 400 guys escaped.)
And it came to pass, when David and his men were come to Ziklag on the third day, that the Amalekites had invaded the south, and Ziklag, and smitten Ziklag, and burned it with fire; . . . And David smote them from the twilight even unto the evening of the next day: and there escaped not a man of them, save four hundred young men, which rode upon camels, and fled. 1 Samuel 30:1, 17
No, Saul was killed by an Amalekite.
I am an Amalekite. ... So I stood upon him, and slew him. 2 Samuel 1:8-10