1)
What is the meaning of "Vayachalosh Yehoshua ... "?
1.
Rashi: It means that Yehoshua severed the heads of Amalek's strong men, keeping alive only the weak ones. He did not kill them all, due to Divine command. 1
2.
Rashbam: It means that he completely vanquished Amalek. 2
1
Lev Eliyahu (p.97): This is because Hashem makes a nation fall only after its Sar (angel) falls. The Sar of Esav will not fall as long as the Yetzer ha'Ra is among us.
2
As in Shemos 32:18 (Rashbam).
