Who are these kings?
Radak #1: They are Nochri kings.
Radak #2: They are Yisrael - all Yisrael are Bnei Melachim (Shabbos 14:4).
Who are Roznim?
Malbim: They are counseling officers.
Why does it say Shim'u regarding kings, and Ha'azinu regarding Roznim?
Malbim: It says Shemi'ah the more important matter, and Ha'aznah about the less important matter.
What should the kings and Roznim learn from this?
Malbim: Do not say that this was a natural matter. I attribute the victory to Hashem and sing to Him.
Why is Anochi repeated?
Rashi citing Midrash Tehilim 68:15 1 : (Har Tavor and Har ha'Karmel came to host Matan Torah, but Hashem disqualified them due to their pride. He said that He would reward them through two salvations, in the days of Devorah and of Eliyahu.) Hashem paid them double. It says at Sinai "Anochi Hashem Elokecha", and it says here Anochi Anochi, and it says at Har ha'Karmel "Hashem Hu ha'Elokim Hashem Hu ha'Elokim."
Only the part in brackets is in our texts of the Midrash.
Why does she mention Shirah and Zemer?
Malbim: Zemer is a higher level than Shirah and adds to it. This is why Shirah is always first, e.g. "Shiro Lo Zamru Lo" (Tehilim 105:2). Zemer praises Hashem for matters of Hashgachah or miracles. The Zemer is attributed to Elokei Yisrael, which hints to the special Hashgachah in Yisrael that publicizes their high level.
