When are these Berachos said?

Tosfos: The Rashbam's text puts the father's Berachah first. He established to do so, for Lehachniso implies the future, like it says in Pesachim (7a) 'all agree that Leva'er is future.' This implies that we bless on all Mitzvos before doing them. R. Tam returned the custom like initially. His text puts the Mohel first, like all our Seforim. The Sugya supports this. All present say 'just like he entered the Bris, he should enter Torah, marriage and good deeds!' This implies that that he already entered! Also regarding a convert, the Mohel blesses, and afterwards the Mevarech blesses '...v'Tzivanu Lamul Es ha'Gerim...' The latter Berachah corresponds to the father's Berachah. We cannot change the order there, for he concludes Kores ha'Bris, which implies after the Bris. Also, the Mevarech always blesses after, like for a baby. Pesachim (7a) means that all agree that Leva'er implies future more than the past. However, it also can mean the past. They argue about Al Bi'ur, if it is primarily the past, or equally the future. We bless on all Mitzvos before doing them, when the Mevarech himself does them. (Here, the Mohel does the Mitzvah, and the father blesses.)

Daf Al ha'Daf: The Shach (YD 264) explains, when he himself does not do the Mitzvah, he blesses after, amidst concern lest the Mohel retract and not circumcise. The Rosh says that he blesses between Milah and Peri'ah; this is considered before the Mitzvah, for Peri'ah is Me'akev. The Shach says, once he circumcised, we are not concerned lest he retract and not do Peri'ah. The Taz wrote, when the father himself circumcises, we are not concerned lest he retract, so he blesses both beforehand.

Daf Al ha'Daf: Tosfos holds that also Lehachniso is a Berachah on the Mitzvah. Beis Yosef (YD 265) bring Rabbeinu Mano'ach's opinion that if the father circumcises, he does not bless it, for we do not find two Berachos on one Mitzvah. Avudaraham says that he does bless; it is for the additional Mitzvah on the father.

What is the significance of Lehachniso bi'Vriso Shel Avraham Avinu?

Teshuvas R. Akiva Eiger (1:42): Olelos Efrayim says, via Milah of the external Orlah, the heart is circumcised, and its chambers are opened to Torah. The Levush says, v'Tzivanu Al ha'Milah is on Mitzvas Milah; Lehachniso bi'Vriso... refers to the father's Mitzvah to teach Torah to his son. Milah enables the son to learn better! If the father died, it is proper for the grandfather to bless, since he has a Mitzvah to teach Torah to his grandson (Kidushin 30a).

Daf Al ha'Daf: Hagahos Maimoniyos (Hilchos Milah 3:3) asked why the father blesses. The Mohel, his Shali'ach, blesses! Moriyah (22:8, p.20, citing R. Yehudah ben ha'Rosh) - Milah is his first Mitzvah. The baby cannot bless, so his father blesses for him. If he was not circumcised until Bar Mitzvah, he circumcises himself and blesses both Berachos. Why does he not bless on teaching his son Torah, and marrying a woman to him? These are due to Milah - 'the one who entered him to Bris, will enter him to Torah, marriage and good deeds!'

What do we learn from 'those who stand there say...'?

Rav Elyashiv: The Mordechai (422) inferred that one should stand at the time of Milah. Daf Al ha'Daf - Teshuvas Maharam mi'Rotenberg (4:154) learned from here, and from "va'Ya'amod Kol ha'Am ba'Bris." Bartenura (Bikurim 3:3) says that workers must stand for those who bring Bikurim, for a Mitzvah is dear in its time; this is why we stand for those who carry the bier or carry a baby to Bris Milah.

Why do they say 'he should enter Torah, marriage and good deeds'? He is obligated in Mitzvos from 13 years; it is proper to marry at 18 (Avos 5:21)!

Rav Elyashiv: 'Good deeds' is not Mitzvos. If so, Torah (which was before) was without Mitzvos. Does he learn without intent to fulfill?! Rather, Torah includes Mitzvos - he learns with intent to fulfill. 'Good deeds' is a trade. One is obligated to circumcise his son, redeem him (if he is a Bechor), teach to him Torah, marry a woman to him, and teach to him a trade (Kidushin 29a). First we bless the father about Mitzvos that he must do to his son - Bris, Torah and marriage' - and afterwards teaching to him a trade, which is the custom. (NOTE: Why does he call it a custom - the Gemara calls it a Mitzvah! Perhaps we do not bless about redeeming him, for usually it does not apply - he is not the Bechor, or one of the parents is a Kohen or Levi, or he was born via Yotzei Dofen. - PF)

Who is the Mevarech?

Piskei Rid: It is the one who blesses on the wine.

Who is Yedid?

Rashi: It is Yitzchak, He is called so based on "Asher Ahavta."

Tosfos: It is Avraham, who is called Yedid - "Mah li'Ydidi b'Veisi" (Menachos 53b). The Berachah mentions all three Avos - Chok bi'Sh'ero Sam refers to Yitzchak, and v'Tze'etza'av Chasam b'Os Bris Kodesh is Yakov and his seed. Targum Yonason of "ha'Tze'etza'im veha'Tzefi'os" is Banya u'Vnei Banya.

Maharal: Kidesh Yedid mi'Beten is Yisrael, who was circumcised on day eight. Chok bi'Sh'ero Sam is Avraham, and v'Tze'etza'av Chasam b'Os Bris Kodesh is Yakov, who was the most Kadosh of the Avos.

Maharal, Maharsha: Am Yisrael are called Yedidim to Hash-m. Also v'Tze'etza'av are Yisrael; the Mitzvah was given to all of them, and not to individuals.

Daf Al ha'Daf: Ohr Zaru'a (107) says that Kidesh Yedid mi'Beten is Yakov, who was born circumcised. Shibolei ha'Leket (Milah 4) says that it is Yakov, for "u'Shnei Le'umim mi'Me'ayich Yiparedu" - this one to his virtue, and this one to his evil.

How was he sanctified from the womb?

Rashi: He was sanctified from the womb for Mitzvas Milah - "Aval Sarah Ishtecha.. va'Hakimosi Es Briso Ito."

Maharal: Every Yisrael is Kadosh from the womb to count to Mitzvas Milah.

Maharsha: "Ha'Amusim Mini Veten" (Yeshayah 46:3).

Iyun Yakov: Yalkut Reuveni (Sof Lech Lecha) says that Avraham was circumcised before Yitzchak was born, so he would be Kadosh mi'Beten.

What is the meaning of Chok bi'Sh'ero Sam?

Rashi: He put the Chok (statute) of Milah in his flesh.

Maharal: Chok is Milah; it does not depart from a person. This is why David sang Shirah over it (Shochar Tov 6); other Mitzvos [sometimes] depart from him.

Maharsha: This is unlike other Chukim, which are not in man's body, like Tefilin and Tzitzis.

Why does it say b'Os Bris Kodesh?

Maharsha: It is an Os Bris, like Hash-m told Avraham "v'Hayah l'Os Bris Beini..." It says Kodesh, for Kedushah is always a fence against Ervah. Milah reduces lust for Bi'ah.

Why does it say Kel Chai Chelkenu Tzurenu?

Maharal: Hash-m is Kel Chai. Life is proper for those who cling to Him.

What is the meaning of Tzivah Lehatzil Yedidus She'erenu mi'Shachas Lema'an Briso?

Rashi: He commanded so to save from Gehinom - "Gam At b'Dam Brisech Shilachti Asirayich mi'Bor Ein Mayim Bo."

Maharsha: It says in Eruvin (19a) that Avraham sits at the opening to Gehinom, and takes out any Yisrael who has no Isur Ervah. If a Yisrael had relations with a Nochris, his foreskin stretches, and Avraham does not recognize him [to save him]. Therefore, it says Lema'an Briso.

Maharal: He commanded His angels to save His dear ones from death, which is called Tzalmaves. Do not say that He commanded Mitzvas Milah to save from death. If so, 'bi'Schar Zeh... Tzivah' is a repetition! Rather, because we have this Mitzvah, He commanded His angels to save His dear ones. Gehinom does not apply to Yakov - he did not die (Ta'anis 5b)! Rather, He commanded to save Yakov's seed.

What is the reason for the Berachah 'Asher Kidesh... Kores ha'Bris'?

Piskei Rid: Even though [the Mohel] already blessed on the Milah, this Berachah was enacted, for this Mitzvah is given to fathers, unlike all other Mitzvos. (NOTE: A father is commanded also to teach Torah to his son! There, also the grandfather is commanded. A father is commanded also to redeem his Bechor! That does not apply to every father, e.g. Kohanim, Leviyim, the Bechor was a girl... - PF)

Why do only the Berachos for Milah of converts and slaves mention that if not for Milah, Shamayim and Eretz would not last?

Ha'Boneh: Seemingly, the Bris was only between Hash-m and Avraham. However, it sustains the world. Now, also they enter the Klal of those who sustain the world!

Where are we commanded to circumcise converts?

Rav Elyashiv citing Tosfos ha'Rosh: We are commanded to love converts. He cannot convert without Milah! If he wants to convert and accepts the Mitzvos, he must circumcise. One who helps him fulfills loving converts.

Where are we commanded to circumcise slaves?

Tosfos: "Yelid Bayis u'Miknas Kesef."

Ha'Boneh: The verse ends "li'Vris Olam" - they enter the Bris that sustains the world!