Why does it say "b'Hatzoso"?
Rashi: This is like "b'Hatzosam Al Hashem" (Bamidbar 26:9; Radak - i.e. 'when he fought.') He fought them, for they helped Bnei Amon [to fight Yisrael - Shmuel II, Perek 10].
Radak citing Shocher Tov: Hetzis (he ignited) fire on them.
Radak citing a Midrash: This is like b'Chatzoso 1 , with a Ches; he put Aram Naharayim in Aram Tzovah and vice-versa.
Tanchuma Devarim 3 connotes that its text of the verse was with a Ches. Mizrachi (Vayikra 19:20) - Hei and Ches are interchangeable, for they are pronounced from the same place (the throat).
Why does it say "va'Yashav"?
Radak: This teaches that there were two wars. Refer to Shmuel II, 8:13:3:3.
Here it says that David killed 12,000 of Edom in Gei Melach. In Tehilim (60:2), it says that Yo'av killed 18,000 of Edom there, and in Divrei ha'Yamim I, 18:12 it says that Avishai killed 18,000 of Edom there!
Refer to Shmuel II, 8:13:3:1-4 and the notes there.