Why is this Sefer among Trei Asar, and not a Sefer by itself?
Radak citing Bava Basra 14b: Chazal combined them into one, lest a Sefer be lost due to its small size.
Why does the Navi give the name of Hoshe'a's father?
Radak citing Megilah 15a: The verse names a Navi's father only if also his father was a Navi. If it names also his grandfather, his fathers were greater than one that only his father was named. Be'eri is Be'erah whom Tiglas Pil'eser exiled; he was Nasi of Reuven.
Do we know which city Hoshe'a was from?
Radak citing Megilah 15a: If the verse tells a Navi's city, he was from there; if not, he was from Yerushalayim.
What was the purpose of his Nevu'ah?
Radak: It was to rebuke Yisrael and Yehudah for doing evil in Hashem's eyes.
What is the significance of Hoshe'a's prophecy spanning the reigns of four kings?
Rashi citing Pesachim 87b: Woe to authority, which buries those who have it!
Who was Yaravam ben Yo'ash, and why is he listed with Malchei Yehudah?
Rashi citing Pesachim 87b: He was from the sons of Yehu. Also he reigned at the time of Uziyah and Yosam 1 . He had a merit to be listed with these Tzadikim ? he did not accept Leshon ha'Ra about Amos. "Va'Yishlach Amatzyah 2 ... El Yarav'am... Kashar Alecha Amos... ; Ko Amar Amos ba'Cherev Yamus Yarav'am." Yarav'am said, surely that Tzadik would not say so! (I am the third generation from Yehu. Hashem promised four generations of kings from him.) And if he said so, Hashem told him to say so 3 !
Malbim: I explained in Melachim II, Perek 15, that from when Yo'ash conquered Amatziyah Melech Yehudah, Malchei Yehudah were submissive under Malchei Yisrael; the kingdom was called on the name of Malchei Yisrael. This was until 24 years into Uziyah's reign, which was Yaravam's 27th year; then, Uziyah strengthened himself and ruled independently. "Bi'Ymei Uziyah" refer to after his 24th year; "uvi'Ymei Yaravam" refers to the first 24 years. Also refer to 1:2:1:1 and the note there.
Rashi brought from Chazal why Yaravam merited to be listed with Malchei Yehudah. What was the question? The verse lists the kings of Yehudah and of Yisrael!
Radak: Chazal asked the question, for Yaravam did not rule with all of these kings; his reign ended in the lifetime of Uziyah, the first of them 1 . Uziyah reigned 52 years. Uziyah became king in Yaravam's 27th year; Yaravam reigned only 14 more years after this! And even according to Chazal (Seder Olam 19), that he and Uziyah began to reign together, he did not reign with the other kings 2 .
Malbim: Normally, Nevi'im are 'attributed' only to Malchei Yehudah; refer to 1:1:6:2.
Therefore it is difficult why only he was listed, but not the other Malchei Yisrael who reigned together with the last three Malchei Yehudah. (PF)
Rashi said that he reigned at the time of Uziyah and Yosam. This is like this Chazal; the 25 years that Uziyah had Tzara'as, Yosam ruled the land (Tosefta Sotah 12:4). (PF)
