BIRKAS HA'MAZON MUST BE RIGHT AFTER MAYIM ACHARONIM [Birkas ha'Mazon: Mayim Acharonim]
Gemara
35b (Mishnah): In the east of the Azarah was Sha'ar Nikanor.
37b (Mishnah): The Azarah was 187 Amos from east to west. Ezras Yisrael was 11 Amos wide, and so was Ezras Kohanim.
Menachos 93b (Mishnah): We slaughter right where Semichah was done. Shechitah is done Tekef to (right after) Semichah.
This means that Shechitah is done at the same place in the Azarah as Semichah because Shechitah is right after Semichah.
Zevachim 33a (Beraisa): Shechitah must always be Tekef to Semichah, except for Asham Metzora, for which Semichah is by Sha'ar Nikanor. The Metzora cannot enter the Azarah until the blood of the Asham is put on him and the blood of the Chatas is Nizrak.
Inference: Bi'ah b'Miktzas is Bi'ah. If it were not, he could stick his hands in and do Semichah!
Rejection (Rav Yosef): The Tana is R. Yosi b'Rebbi Yehudah, who says that Tzafon (the north part of the Azarah, where we slaughter Asham) is far from the end of Sha'ar Nikanor.
Berachos 42a (R. Chiya bar Ashi): Shechitah must be Tekef to Semichah, Tefilah (Shemoneh Esre) must be Tekef to Ge'ulah (Ga'al Yisrael), and Berachah must be Tekef to Netilas Yadayim.
Berachos 51b (Rav Asi): One may not talk on the Kos Shel Berachah.
51b (Mishnah -Beis Hillel): First we mix the cup, then we wash the hands.
52b: They permit using a cup whose outside is Tamei, so we are concerned lest the cup be Metamei wet hands. Also, one must eat Tekef to washing.
Pesachim 106a (Rav Berona citing Rav): One who washed his hands should not say Kidush (it is a Hefsek (interruption) between washing and ha'Motzi. Rather, he hears Kidush from someone else.)
115a (Rav Chisda): (Even though) one washed his hands for the first dipping (at the Seder), he washes for the second dipping.
Question: Why must he wash again? He already washed (knowing that he will dip again)!
Answer: Since we say Hagadah and Hallel in between, perhaps he was distracted and touched (something that is Metamei the hands).
Rishonim
Rif (Berachos 30a): Even after the table was removed, one may eat. We do not hold like the teachings here. (On 42a, some forbid eating after the meal, or after the bread was taken away...) Rather, as long as he did not wash, he may eat. Berachah must be Tekef to washing.
R. Yonah (DH Sheloshah): R. Zeira omitted that one must eat Tekef to washing, for he lists only matters learned from verses.
R. Yonah (38a DH Ein): Rashi explains that the Mevarech may not talk from when they give the cup to him. He must start to bless immediately. Tosfos (Berachos 51b DH Ein) says that if others are Yotzei through him, even though they do not hold a cup, also they may not talk.
Rambam (Hilchos Berachos 6:20): One says Birkas ha'Mazon Tekef to Netilas Yadayim. He does not interrupt at all. He may not even drink water until blessing Birkas ha'Mazon.
Kesef Mishneh: The Rambam and Rashi (Berachos 42a DH l'Netilah) forbid eating after Netilas Yadayim. This connotes that one may speak afterwards. They did not explain that 'Berachah must be Tekef to Netilah' forbids speaking, for we forbid speaking (only) from when they mixed the Kos Shel Berachah (51b). This implies that until then (even after Netilas Yadayim), one may speak.
Rambam (7:15): One may not talk on the cup of Birkas ha'Mazon. Rather, everyone is quiet until they finish Birkas ha'Mazon and drink the wine.
Rosh (Berachos 6:31): Berachah must be Tekef to Netilah. Some distinguish between eating and drinking (and allow drinking after Mayim Acharonim). This is unreasonable.
Rosh (7:35): Rav Asi taught that one may not talk on the Kos Shel Berachah. Rashi explains that the Mevarech may not talk from when they give the cup to him. It seems that similarly, the others at the meal may not talk from when he starts to bless.
Rashi (Zevachim 33a DH Merchak): The Tana holds that Tzafon is only to the north of the Mizbe'ach, which is 22 Amos west of Sha'ar Nikanor. Therefore, it is impossible to do Semichah from the Ezras Nashim, and Tekef l'Semichah is Shechitah in the north.
Tosfos (Sotah 39a DH Kol): Our Gemara says that "lift your hands in Kedushah and bless Hash-m" discusses Birkas Kohanim. The Yerushalmi holds that it discusses Mayim Acharonim. Berachos 42a connotes similarly. We can learn the Shi'ur of Tekef from Shechitah of Asham Metzora, which cannot be Tekef to Semichah, which is by Sha'ar Nikanor. Midos 37a connotes that they are only 22 Amos apart.
Poskim
Shulchan Aruch (OC 165:2): If many are at a meal, the Gadol washes first. The Rosh used to wash last, in order that he not interrupt or speak.
Magen Avraham (4): All agree that 'Berachah is Tekef to Netilah' refers (at least) to Mayim Acharonim, yet one may talk between Mayim Acharonim and Birkas ha'Mazon! We forbid (183:6) only after one picked up the cup to bless! Perhaps the Shulchan Aruch forbids (discussing) another matter, which is a Hefsek, but two or three words is not a problem. All the more so, if asked something, one may answer yes or no.
Machatzis ha'Shekel: He asks that since we are more lenient about a Hefsek after Mayim Rishonim (washing before the meal), all the more so a few words should be permitted! Below (179:1), the Magen Avraham forbids. Here the Magen Avraham explains the Kesef Mishneh, Rosh and Shulchan Aruch (but he himself forbids).
Shulchan Aruch (166:1): Some say that one need not be careful about a Hefsek (interruption) between Netilas Yadayim and ha'Motzi. Some say that one must be careful. It is good to be careful.
Beis Yosef (DH u'Mah): The Yerushalmi says that one who blesses right after Netilas Yadayim will not be harmed the entire meal. This implies that it discusses Mayim Rishonim. It cannot refer to Mayim Acharonim, for he already finished the meal. What was, was! (This will not change whether or not he was harmed during the meal.) It is good to be careful also about Mayim Rishonim.
Gra (2): The first opinion explains that if one blesses right after Mayim Acharonim, the Satan does not prosecute about the meal.
Rema: If one delayed the time to walk 22 Amos, this is called a Hefsek.
Taz (2): The Maharshal (Teshuvah 34) says that this is only for Mayim Acharonim. For Mayim Rishonim, it is merely good to be careful (to avoid a delay).
Kaf ha'Chayim (7): Even a small amount of talk, even Divrei Torah, is a Hefsek. The Magen Avraham (179:1) connotes like this (regarding Mayim Acharonim).
Kaf ha'Chayim (9): We are not concerned if he took a long time to dry his hands, for one must dry them well. The same applies to Mayim Acharonim, for one must dry his hands before blessing.
Shulchan Aruch (179:1): When one finished the meal and washed Mayim Acharonim, he may not eat or drink before blessing Birkas ha'Mazon.
Beis Yosef (DH v'Yesh): I say that the Isur to eat or drink is because one must bless Tekef to Netilah. One washes in order to be ready to bless. It is as if he already started blessing. This does not apply to one who merely said 'let us bless.' Then the only problem is Hesech ha'Da'as, so he may say a Berachah Rishonah and eat more. Therefore, one should not talk between Mayim Acharonim and blessing. Even the Rosh, who says that one must bless Tekef to Netilah' refers to Mayim Rishonim, holds that it applies also to Mayim Acharonim.
Taz (1): I say that if one wants to eat or drink after Mayim Acharonim, and afterwards he will wash again, he may. He will fulfill 'Berachah is Tekef to Netilah'! The first washing is considered like mere water, and not Mayim Acharonim. One cannot say that it is as if he already began blessing. Even if he prepared himself why can't he retract?! The Rema (197:1) equates saying 'let us bless' and Mayim Acharonim.
Magen Avraham (1): One may talk after Mayim Acharonim, and so the Shulchan Aruch connotes below (183:6, like he said in the Kesef Mishneh, that we forbid (only) after one was given the cup of Birkas ha'Mazon). In 166:1, the Shulchan Aruch forbids (between Mayim Rishonim and blessing; all the more so one may not talk between Mayim Acharonim and blessing). His proof to permit is invalid. The Gemara forbids after they mixed the cup, even if he did not wash yet. (However, Netilas Yadayim itself forbids speaking afterwards!)
Eshel Avraham (1): The Beis Yosef (and Shulchan Aruch) here forbids talking in between. He learns from the Rosh. In Sefer Kesef Mishneh, he derived that the Rambam permits. One may interrupt with an action, even if he will wash again. The Magen Avraham says that even the Rambam could forbid talking.
Mishnah Berurah (1): Also, one must be careful not to interrupt with talk, even a little, for Berachah must be Tekef to washing. Therefore, one should not delay a lot after washing, and surely not engage in something. If necessary, one may interrupt for an urgent need. B'Di'eved, if he interrupted, he washes again, so the Berachah will be Tekef to washing.
Mishnah Berurah (2): The Acharonim are lenient to say ha'Motzi and eat after Netilas Yadayim, just he must wash Mayim Acharonim again afterwards. Some say that l'Chatchilah one should be stringent. The leniency is only to eat, but not to speak or engage in something else.
Kaf ha'Chayim (4): Even if he is sure that he guarded his hands, it does not help.
Shulchan Aruch (183:6): From when they give the cup to the Mevarech (the one who says Birkas ha'Mazon), he may not talk. The others may not talk from when he begins to bless.
Beis Yosef (DH u'Mah): R. Yonah and R. Yerucham forbid all to talk from when they give the cup to the Mevarech. It seems that the Tur disagrees.
Magen Avraham (10 and Mishnah Berurah 22): One should be stringent like R. Yonah and R. Yerucham.
Kaf ha'Chayim (32): The Ari Zal says that he should not take the cup until Mayim Acharonim and saying the verses before Birkas ha'Mazon. Already from then one may not talk.