Why does it say that only one Shevet will remain to David's seed? They retained both Yehudah and Binyamin!
Radak (here and 12:20): They are considered like one Shevet, for both had parts of Yerushalayim. Whoever rules over Yerushalayim will surely rule over both of them.
Why does it say "David Avdi"? Verse 12 said "David Avicha"!
Malbim: This will not occur in Shlomo's lifetime due to Hashem's promise to David about his son. One Shevet will remain because David is Avdi, and his throne is like the sun in front of Me.
Why is it due to Yerushalayim?
Malbim: It says "Gam Beneihem Adei Ad Yeshvu l'Chisei Lach; Ki Vachar Hashem b'Tziyon" (Tehilim 132:12-13). Through choosing Yerushalayim, the throne will remain for David, who built Tziyon.
