Did the gates truly sink in the ground?
Rav Sadya Gaon: No. It is as if they already sank.
Rashi citing Eichah Rabah 2:13: Yes, because they showed honor to the Aron - "Se'u She'arim Rosheichem... 1 " (refer to Tehilim 24:7:1:1). Therefore, no person overcame them. Palgei Mayim - this shows how great is the reward of Torah. We find that Hashem pardoned idolatry, but not Bitul Torah (Yerushalmi Chagigah 1:7).
Rashi citing Sotah 9a: Because David made them 2 , the enemy could not overcome them.
R. Avigdor citing Eichah Zuta 1:7: Yes. The Tes is small, for the gates of Yerushalayim were shrinking from Rosh Chodesh Av, and on Tish'ah b'Av they were small [enough to let the enemy enter 3 ]. Yirmeyah's uncle Chanam'el used Hashem's name to raise Yerushalayim in the air [lest the enemy destroy it]. Hashem 'kicked' it back down, and the gates were swallowed in the ground.
Ri Kara: No. From when "Chel v'Chomah" ceased (8), the gates and bolts are futile. No one is concerned to build them, so automatically they perish.
Shabbos 30a implies that this refers to the gates of the Kodesh ha'Kodoshim, i.e. the doors of the opening in the wall between it and the rest of the Heichal (Melachim I, 6:31) (PF). This is unlike Rashi's other Perush (refer to 2:9:1:3 and the note there).
Rashi (9a): The gates of Metzudas Tziyon (Ir David) were of copper or gold. They sunk, lest the enemy take them.
Eichah Zuta 1:7, partially cited in R. Avigdor: Chanam'el used Hashem's name to bring down armed angels; the enemy fled. Hashem changed the angels' names [and they departed].
Were the bolts broken and lost?
Rav Sadya Gaon: It is as if He already broke them, until they perished. Ibn Ezra - the subject is Hashem; He was mentioned in verse 8.
Palgei Mayim: They were broken, lest they prevent the gates from sinking in the ground.
Refer to 2:9:1:5.
What do we learn from "[Malkah v'Sareha va'Goyim] Ein Torah"?
Rav Sadya Gaon: Without Torah, "Gam Nevi'eha Lo Matz'u Chazon me'Hashem" (even Nevi'im did not find a vision from Hashem) [Ibn Ezra - in a foreign land].
Rashi: No one gives rulings [in Halachah].
Ibn Ezra: When the gates sank, the king was exiled without the extra Sefer Torah that he must carry with him at all times.
Rid: Amidst the Goyim, they cannot engage in Torah.
Ri Kara: From when the king and officers were exiled, Torah does not last in Yisrael. All the Mitzvos that depend on the land do not apply. Also, the nations make decrees on them to nullify the Torah.
Palgei Mayim: The enemy was able to rule over the king and officers due to Bitul Torah. There was Bitul Torah even when Nevi'im did not receive Chazon (harsh prophesies), rather, they had good.
What do we learn from "Gam Nevi'eha Lo Matz'u Chazon me'Hashem"?