Why does the Torah repeat the words, "b'Etzem ha'Yom ha'Zeh" at the beginning of this Pasuk, having already mentioned them in Pasuk 17:23?
Rashi: To teach us that Avraham was circumcised at the end of his ninety-ninth year (i.e. at his 99th birthday), and Yishmael at the end of his thirteenth year. 1
Ramban: It teaches us that Avraham circumcised all 318 members of his household on the same day that he circumcised himself and Yishmael - another lesson in his Zerizus.
Da'as Zekenim, Kli Yakar (citing Pirkei d'Rebbi Eliezer): We learn from here that Avraham was circumcised on Yom Kipur 2 (about which the Torah (Vayikra 23: 28-30) uses the very same term, "b'Etzem ha'Yom ha'Zeh"). 3
Moshav Zekenim asks: Midrash Shir ha'Shirim learns from "k'Chom ha'Yom" (Bereishis 18:1) that Avraham's Milah was in Tamuz! (However, this does not appear in our versions of the Midrash. How would the Midrash explain "la'Mo'ed... ka'Es Chayah" (18:14)? Yitzchak was born on Pesach, which would neither be the next Mo'ed, nor the same time next year! - PF) (Perhaps the text of the Midrash should read, " 'K'Chom ha'Yom' - as hot as if it were Tekufas Tamuz" -when in fact it was not Tamuz, but Nisan (or Tishrei - refer to 17:26:1.1:1)) (CS).
Whom did Avraham circumcise first - himself, or the members of his household?
Ramban: Surely Avraham circumcised everyone else first (or personally oversaw other Mohalim that did so), and then circumcised himself last. After his Milah he would be in pain or sick, and unable to carry out the Mitzvah. This is implied by 17: 23-24, where it mentions Yishma'el's Milah and those of Avraham's household before his own. 1
Ohr ha'Chayim (to 17:23): Avraham circumcised himself first. The verse "Himol Yimol" (17:13) teaches that only one who himself is circumcised may circumcise others. 2
Rosh (to 17:13) Avraham tried to circumcise several members of his household first, and failed to do so safely. Mamrei gave Avraham the advice to circumcise himself first, after which he was able to perform the Milah on others. 3
Da'as Zekenim, Pirkei d'Rebbi Eliezer (29): Avraham summoned Shem ben Noach to perform his Milah (and that of Yishma'el). 4
This is also the opinion of Ibn Ezra, as well as Radak to 17:23.
Avodah Zarah 27a; Targum Yonasan to 17:13. To resolve the opinion of Ramban, see Answer 4. Perhaps Avraham employed numerous people who were born circumcised, or were circumcised through such people. Some hold that females can circumcise males (PF).
Shem ben Noach had been born circumcised - Bereishis Rabah 26:3; Rashi to 5:32 (CS).
QUESTIONS ON RASHI
Rashi writes: "'On this very day' - [when] Avraham reached 99 years old... he was circumcised." Ramban asks - The Halachah follows Rebbi Eliezer, that the world was created in Tishrei, and the Avos (other than Yitzchak) were also born in Tishrei (Rosh Hashanah 10b). It emerges [from this Rashi] that Avraham's Bris Milah was in Tishrei. However, Rashi (to 18:10) writes that [two days later,] Avraham would be informed of Yitzchak's upcoming birth - on Pesach! If so, Avraham's Milah was in Nisan?
Gur Aryeh: According to Rebbi Eliezer, the Avos were born in Tishrei; and the Milah and the news of Yitzchak's impending birth, were also in Tishrei. (Refer to 17:21:151:1:1. Yitzchak would be born about six months later, in Nisan.) When Rashi to 18:10 writes that Avraham was informed in Nisan, he follows the opinion of Rebbi Yehoshua (Rosh Hashanah 11a), that the world was created in Nisan, all the Avos were born in Nisan, and so Avraham's Milah was also in Nisan. 1
Rashi writes: "'On this very day' - that Avraham reached 99 years old, and Yishma'el reached 13 years old, they were circumcised." Ramban asks - what does this teach us?
Gur Aryeh: Prior to Matan Torah, one became liable to punishment at the hands of Heaven only at 100 years old. The Torah tells us that HaSh-m commanded Avraham in the Mitzvah of Milah on this exact date, for it was not fitting that Avraham should even begin his 100th year without Milah. Yet, even prior to Matan Torah, a minor would leave his father's control at age thirteen. Had Yishma'el reached that age, whether to perform this Mitzvah would have been up to him, and he would never have performed it. 1
Gur Aryeh: The commandment of Milah had not been addressed to Yishma'el personally, but rather to Avraham [and that command included the members of his household].