Were all 14 days called Chag?
Radak: Yes - also the days of inauguration were called Chag, because they were next to Sukos.
Malbim (Divrei ha'Yamim II, 8:8): Perhaps Ezra wrote in Divrei ha'Yamim only "Shiv'as Yamim" to teach that the seven days before Sukos were not called Chag, and Melachah was permitted. If so, we can say that they fasted on Yom Kipur; Chazal expounded unlike this.
Why does it say "mi'Levo Chamas Ad Nachal Mitzrayim"?
Rashi: Levo Chamas is in the north of Eretz Yisrael. Nachal Mitzrayim is opposite it, in the south.
Why does it say "seven days and seven days, 14 days"?
Rashi: Seven days were for inauguration [of the Mikdash], and seven days were Chag ha'Sukos.
Radak: From "14 days" we infer that there was no break in the middle. "He sent the nation on the eighth day" was Shemini Atzeres. You cannot say that first was Sukos, and then seven days of Chanukas ha'Bayis, and he sent the nation on the eighth day of Chanukas ha'Bayis, for Divrei ha'Yamim II, 7:10 says that he sent them on the 23rd!
QUESTIONS ON RASHI
Rashi writes that seven days were for Chanukah, and [after] seven days of Sukos. If so, Yom Kipur was among the days of Chanukah. Did they eat and drink on Yom Kipur?
Rashi: Yes. Radak - Mo'ed Katan 9a says so. They learned from Chanukas ha'Mishkan, which permitted offering Shelamim on Shabbos, for which one is stoned. All the more so [Chanukas ha'Bayis] permits the Isur Kares of Yom Kipur! Do not say that they offered Shelamim, but did not eat them. Simchas ha'Guf is only with eating and drinking!
Radak: Perhaps they did not eat. One who eats or drinks on Yom Kipur is Chayav Kares! Even though the inauguration was seven days, and every day they offered Shelamim, including Yom Kipur, they did not eat them until the night or the next day 1 .
On Yom Tov we may offer only Korbanos Tzibur with a fixed time. If a Hora'as Sha'ah permitted offering Nedavos on Yom Kipur, perhaps it permitted also eating them! There is Kares also for Melachah on Yom Kipur! (PF)
