What is the meaning of "Ra'u Halichosecha Elokim"?
Rashi (from Tanchuma Yashan Beshalach 13): It is proper for You to save these, for when they saw Your ways in Kodesh at the Yam [Suf], they sang first in front of You Shiras ha'Yam, and afterwards ha'Nognim, i.e. the angels.
Radak: When Yisrael saw the enemy stricken, they recognized that these are Your ways, that You went in front of them and struck the enemy.
Malbim: After defeating the enemy in war, Hashem, the Head of the legions, returned with His nation to Eretz Yisrael, and they sang to Him in gatherings. First the metaphor resembles Moshe's words "va'Yhi bi'Nso'a ha'Aron" (Bamidbar 10:35), and now in His return, it is like "uv'Nuchah Yomar Shuvah Hashem Rivevos Alfei Yisrael" (ibid., 36). Myriads of Yisraelim came to greet Him with Tupim (drums, or tambourines) and dances, when they saw Your ways in Kodesh. I.e. You returned to Eretz ha'Kodesh.
Why does it say "Halichos Eli Malki va'Kodesh"?
Radak: He is King in Shamayim, which is the Kodesh place, and He sent His angels to help Yisrael - "va'Yetzei Mal'ach Hashem va'Yach b'Machaneh Ashur" (Melachim II, 19:35).
Malbim: Refer to 68:25:1:3.
