What is the meaning of "Bila"?
Rid: He destroyed, like "Bila ha'Maves" (Yeshayah 25:8).
What are "Ne'os Yakov"?
Rav Sadya Gaon: The dwellings of Beis Yakov. Rashi - Ne'os is like "Neve [Kodshecha]" (Shemos 15:13). Ibn Ezra - the Aleph is in place of a Vov, like "Nevos Keros Ro'im" (Tzefanyah 2:6). Also "Tesa'u Lachem" (Bamidbar 34:7, has an Aleph in place of a Vov.)
R. Avigdor citing Eichah Rabah 2:4: This refers to Adaryainus Kaiser, who had 80,000 horn-blowing [officers], and each was appointed over 100 soldiers. Ben Kuziva [led the Jewish army. Initially, each [soldier] had a truncated Etzba 1 (he would bite off a finger to prove his Gevurah. Chachamim) rebuked him, and told him to test their Gevurah via ability to uproot a cedar of Levanon 2 . He had 400,000 3 soldiers, and they told Hashem 'do not help us, and do not prosecute against us' - "ha'Lo Atah Elokim Zenachtanu v'Lo Setzei Elokim b'Tziv'oseinu" (Tehilim 108:12). Adaryainus killed so many in Beitar that the blood carried rocks of 40 Sa'im (the size of a Mikveh) four Mil to the sea.
Alei Tamar (Ta'anis 4:5): Etzba can mean toe. He tested them if they would run barefoot on mountains without concern for stubbing their toes on rocks; due to this, parts of toes came off.
This is difficult. A Jewish army needs Tzadikim who trust in Hashem, and not in their physical strength! "Va'Yomer Hashem El Gid'on Rav ha'Am Asher Itach
What are "[Mivtzerei] Vas Yehudah"?
Rav Sadya Gaon: [The fortresses of] the congregation of Beis Yehudah. Palgei Mayim - it was Chesed Hashem not to strike Bnei Yisrael at first, rather, only their houses and fortresses.
Why does it say "Higi'a la'Aretz"?
Rashi: He lowered them to the ground.
Palgei Mayim: He was giving Yisrael a chance to repent. He calmed His anger via destroying the Bayis. There was no punishment to Yisrael themselves, just profaning of the king and officers.
What are "Mamlachah v'Sareha"?
Rashi: Mamlachah are Yisrael, who are called "Mamleches Kohanim" (Shemos 19:6). Sareha are officers above; Hashem switched them. The one who was appointed over fire, He appointed it over water, for there were evil Yisraelim who knew Hashem's explicit name. They were confident that they can impose oaths on officers above to save them from fire, water and the sword. After Hashem switched them, when they imposed an oath on the officer of fire [or anything else], he said 'I am not appointed over it.'
Ibn Ezra: The king [was profaned via lowering the castles, for they used to live in them].