What is the meaning of "Sha'alu Shelom Yerushalayim?
Rashi: Those who love it should have serenity, and its Cheil should have Shalom (7; refer to 122:7:1:1-2).
Radak: Bnei Galus say, ask from Hashem the Shalom of Yerushalayim, i.e. the gathering of exiles. It will not have Shalom until then, for Yishmaelim and Arelim fight against it.
Malbim: The Shalom of a person depends on his limbs and faculties, if they are b'Shalom together. When they are divided, there is death. Also Yerushalayim, which is the unity of the nation, its Shalom depends on the inner serenity of its lovers and their harmony.
Why does it switch from Shalom to Shalvah?
Malbim: Shalom is external; Shalvah is internal.
Who are its lovers?
Radak: They are Yisrael in Galus, who mourn its destruction.
Malbim: This refers to inner love between Yisraelim. It leads to external Shalom of Yerushalayim, even if it will not have Shalom from external enemies.