What do we learn from "ha'Shir Yihyeh Lachem k'Leil Hiskadesh Chag"?
Pesachim 95b: We sing Hallel while eating Pesach Rishon, but not while eating Pesach Sheni. Song is required only if the night has Kedushas Yom Tov (Isur Melachah).
Erchin 10b: Even though Rosh Chodesh has Korban Musaf, and it is called Mo'ed, it does not require Hallel 1 . Song is required only if the night has Kedushas Yom Tov.
Rashi (from Shocher Tov 1:20): This Simchah (the demise of Machaneh Ashur) will come on Pesach night, like you sang the Shir of Pesachim in Egypt. The verse seems to teach about Sancheriv, and teaches about Pharaoh; they sang Hallel when they ate Pesachim.
Radak: On the day of the plague in Machaneh Ashur, the Simchah of Anshei Yerushalayim will be like that of the night of the Chag in which people rejoice and sing.
Malbim: Hashem struck Machaneh Ashur while Yisrael sang Hallel in the Mikdash 2 over eating Pesach. Just like there was great Simchah amidst Yisrael, there was great panic amidst Machaneh Ashur.
Whenever we say half-Hallel, it is a mere custom. (PF)
Kodshim are eaten while sitting. Tosfos (Yuma 25a) implies that this is permitted in the Mikdash only for Kodshei Kodoshim, but not for Pesach, which may be eaten at night anywhere in Yerushalayim! Why does he say that they ate in the Mikdash? (PF)
Why does it add "v'Simchas Levav"?
Radak: Shir is in the mouth; Simchah is in the heart.
Who is "Holech b'Chalil"?
Rashi: People who bring Bikurim, someone plays the flute in front of them to come to Har Hashem (Radak - the Beis ha'Mikdash), like it says in Bikurim 3:3.
Radak: One who truly goes with a flute, he has Simchah of the heart. People who dance in Mechol (a circle), each man by his colleague; the flute is sounded in the middle.
Malbim: There is Simchah due to the time, like Simchah ha'Regel, and Simchah due to what depends on the time, e.g. ascending for the Regel, in order to 'see' Hashem face. Here the Simchah was double (both of these) - k'Leil Hiskadesh Chag, and k'Holech b'Chalil Lavo v'Har Hashem.
Why does it say "El Tzur Yisrael"?
Radak: Hashem was their rock and strength against Melech Ashur.
