When is "that day"?
Radak: It will be at the time of salvation.
Malbim: It will be in the future - or, it was fulfilled in the days of Chizkiyah.
Why will they sing specifically in Yehudah?
Radak: The war and salvation will be there.
What is the meaning of "Ir Az Lanu Yeshu'ah Yashis"?
Rashi: The city of Yerushalayim, which was always a fortress of salvation for us, the Savior will establish its walls and Chel.
Malbim: When many of the 10 tribes return in the days of Chizkiyah, they will say, Yerushalayim is a fortress for us. However, its walls are not fortified via man's building. Rather, Hashem will be its wall and fortification.
What is "Chel"?
Rashi (from Pesachim 86a): It is a low wall in front of the tall wall.
Radak: It is a depression dug out around the wall. The Targum of Ge (40:4) is Chilya.