Why should Bas Tziyon rejoice?
Malbim: Hashem removed your Mishpat. The judges and their crooked judgments departed - "v'Ashivah Shofetayich keva'Rishonah...; Tziyon b'Mishpat Tipadeh" (Yeshayah 1:26-27). This will fix Tziyon.
To whom does "Yisrael" refer?
Radak: It is the 10 tribes.
Malbim: It is the Klal of the nation. Until now there were evil judges in Tziyon. They helped to destroy the city via tilting judgment, oppression and theft. Evil came out in Yerushalayim from the evil kings. The nation moaned because the enemies (other nations) pressured them. Yisrael should rejoice, for the enemy departed. No one will afflict Yisrael.
Why does it say "Simchi v'Alzi"?
Radak: The matter is repeated in different words to strengthen the Simchah.
Is Bas Yerushalayim not Bas Tziyon?
Radak: They are the same; The matter is repeated in different words.
Malbim: Bas Tziyon is where the Sanhedrin, judges and officers reside. Yerushalayim is the capitol - conduct is from there.