1)
What is the meaning of "va'Yachalosh 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 the 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 angel has fallen, and the angel of Esav will not fall as long as the Yetzer ha'Ra is among us.
2
As in Shemos 32:18 (Rashbam).