Why does it say that the moon will be bright like the sun?
Malbim: Affliction is compared to night, and relief to day. Relief at the time of the affliction is compared to light of the moon, which shines in the middle of the night. Success that shines on one's head at the time of good and serenity is compared to sunlight. The moonlight, i.e. the beginning of the salvation, will be as great as sunlight; people will immediately forget the afflictions.
It says "v'Chofrah ha'Levanah u'Voshah ha'Chamah" (24:3 - they will be dim). Here it says that they will be astoundingly bright!
Sanhedrin 91b #1: In Yemos ha'Mashi'ach they will be bright. In the world to come they will appear dim (due to the great radiance of Tzadikim).
Sanhedrin 91b #2: Both refer to the world to come 1 . In the place of Tzadikim they will be bright; in the place of the Shechinah they will appear dim.
So the Gemara answers for Shmuel, who says that the only difference between this world and Yemos ha'Mashi'ach is that the kingdoms will cease to rule over Yisrael. (PF)
How bright is "Shiv'asayim k'Or Shiv'as ha'Yamim"?
Rashi, Mahari Kara: It is seven times seven (49) as much as the light of the seven days of creation, i.e. 343 times as bright 1 [as one day].
Radak #1: This is a metaphor for the great good that they will have in the days of Mashi'ach.
Radak #2: We can say that this refers to the days of Chizkiyah. They will have great good after the death of Machaneh Ashur and the salvation from it. Just like affliction is called darkness - "Shemesh v'Yare'ach Kadru v'Chochavim Asfu Nagham" (Yo'el 2:10), so the salvation is called light - "la'Yehudim Haysah Orah v'Simchah" (Esther 8:16). The light of the sun and moon did not increase. Shiv'asayim is many great lights. Also "Shiv'asayim Yukam Kayin" (Bereishis 4:24) is many vengeances, not only two times seven. Seven comes to increase the count; [it is not precise,] like "Sheva Yipol Tzadik v'Kam" (Mishlei 24:16), "Sheva k'Chatoseichem 2 " (Vayikra 26:21). "K'Or Shiv'as ha'Yamim" is a metaphor. It is as if each of the seven days of the week will be brighter than the previous day.
Radak #3: Shiv'as ha'Yamim are the seven days of Chanukas ha'Bayis in the days of Shlomo.
Malbim: These are the seven known days, of Bereishis. Light shined on the new creation that came into existence. So the light of success will shine on a new world in beauty - the great good will be like a new creation.
What is "b'Yom Chavosh Hashem Es Shever Amo"?
Radak #1: It is the day of gathering of exiles.
Radak #2: It is the war of Gog and Magog. There will be no more afflictions after "Yom Hereg Rav" (25).
Radak #3: It is when Machaneh Ashur was killed in the days of Chizkiyah. Also the Rambam says so.
Malbim: The verse depicts the nation at that time like one whose bones were broken, with pains and wounds. First one must bandage the break, and afterwards heal the external wound. So the inner breakage [of the Nefesh] will be bandaged, and the outer affliction will be healed (bodily success).