Why did he say "va'Yishlachacha"?
Malbim: You said that you wanted to offer them for Korbanos. You should have thought what Hashem, who sent you, wants! One must be more meticulous to fulfill all details of a great matter. Three aspects determine the greatness of a matter, and here they were all great - the doer (you are king), the commander (Hashem), and the action [to eradicate Amalek, the sinners]. Also, your kingship depended on this!
Why does it say "Ad Kalosam Osam", with a Mem at the end of Kalosam?
Rashi: Until the nation with you will eradicate them. Radak - the Mem at the end of Kalosam refers to the doer (Yisrael).
Radak: The Mem refers to the object (it is in place of Osam); it says also Osam for extra clarity.
Malbim: The Mem refers to the object; it says also Osam, for you must totally wipe them out.
