Why does it say "va'Ya'al David"?
Rashi: This is present tense. He did so regularly.
Who was left from Amalek? Sha?ul killed all of them less than two years ago!
Si'ach Mordechai: The Zohar says that via witchcraft, Amalek changed themselves to animals. Perhaps later, they changed themselves back to people. 1
Ho'il Moshe: Sha?ul killed Amalek only "me'Chavilah Bo'acha Shur" (15:7), where they had fixed residences. He did not kill those elsewhere. His sin was rushing to glorify himself, rather than pursuing Amalekim elsewhere 2 .
Hadras Kodesh: Sha?ul was commanded to eradicate "Es ha'Chata'im Es Amalek" (15:18). The Griz (161) says that this is the Rambam's source (Hilchos Melachim 6:4) that if Amalekim accept their seven Mitzvos, we do not kill them. There was no Mitzvah to kill Amaleki Gerei Toshav. Because Sha?ul left alive Agag, these Gerei Toshav later sinned and became like regular Amalekim.
Why does it say "Yoshvos ha'Aretz Asher me'Olam"?
Radak: Those families were there from of old, so they were not guarded. David struck them and took great spoils, and no one knew who did so, for he did not leave a man or woman alive (verse 9).
Malbim: Since they lived there, they had conflicts with Pelishtim, and Pelishtim would not object if David strikes them. 1 They were there from the days of Yehoshua. They were from the seven nations, so David fulfilled "Lo Sechayeh Kol Neshamah" (Devarim 20:16).
Even though David told Achish that he despoils places in Yisrael (verse 10), if Achish learned the truth, he would not be upset. (PF)
What is "Bo'acha Shurah"?