What is the meaning of "va'Ymaded ba'Chevel Hashkev Osam"?
Radak, Mekabel: He made them lie on the ground in the way of vengeance and disgrace (refer to 8:2:2:1. Yonason translates Chevel as 'Adva', i.e. lottery and portion.
Why did he kill two thirds of them?
Rashi (from Bamidbar Rabah 14:1): Because they killed his parents and brothers 1 . It says "va'Yanchem Es Pnei Melech Mo'av" (1:22:4, when he fled from Sha'ul), and we do not find that they left there.
Radak: Except for one brother, whom Nachash ha'Amoni kept alive. This was David's intent when he said "Ka'asher Asah Aviv Imadi Chesed" (10:2).
Why did he keep a third alive?
Malbim: He kept the Giborim alive, to pay a tax.
What is the meaning of "Nosei Minchah"?
Targum Yonasan: Natlei Peras. Radak - i.e. they paid a known tax every year.