Why did he say "la'Shem ha'Yeshu'ah"?
Rashi: It is upon Him to save His servants and His nation.
Radak: Salvation is from Hashem. One is not saved without Him.
Malbim: The war was against Am Yisrael, and there was a great Magefah (plague, i.e. many deaths) in the nation. David requested that many [more] Yisraelim should not die in the war. And so it was - through the killing of Avshalom, the war ceased.
Why does it say "Al Amecha Virchasecha"?
Rashi: It is upon His nation to bless and thank Him.
Radak: Your nation should not die in this war.
Ba'al ha'Turim: It says Birchasecha also regarding Yitzchak's Brachah of Yakov - "va'Yikach Birchasecha" (Bereishis 27:35). From that, his children have this Brachah.
Malbim: [Since the salvation is from Hashem,] I request that Your Brachah remain on Your nation, and they not die in the war.
