things that must be done immediately
What Berachah must be Tekef to washing hands?
Rashi: Birkas ha'Mazon must be Tekef to washing Mayim Acharonim.
Tosfos: Once he washed, he may not eat before blessing. The same applies if he said 'let us bless', even if he did not wash.
Rav Elyashiv: Rashi implies that he may not eat before Birkas ha'Mazon, even if he would bless on what he wants to eat. Acharonim support this from the Gemara's words 'Asur mi'Le'echol.' If he said 'let us bless', he may bless on food and eat it before Birkas ha'Mazon.
Rav Elyashiv: Below (52b), it says that Seudah is Tekef to Netilas Yadayim. Tosfos there asks why this was not taught here. Daf Al ha'Daf - R. Akiva Eiger says that the Midrash and Yerushalmi say that 'Berachah must be Tekef to Netilah' means before the meal. Shulchan Aruch (165:2) brought that the Rosh would wash last, lest he delay in between. He almost never brings the conduct of a Posek! Sefer 'R. Yosef Karo' explains, since the Rif and Rambam hold that our Gemara discusses only Mayim Acharonim, he ruled like them (according to his Klal), but he brought the Rosh's practice, like the simple reading of our Gemara.
Daf Al ha'Daf citing Sho'el u'Meshiv (5 Yosef Da'as 18): Our Gemara omitted Seudah is Tekef to Netilas Yadayim, for it discusses matters that apply only on weekdays, but not on Shabbos. There is no Semichah on a Korban on Shabbos. One need not be Somech Ge'ulah to Tefilah on Shabbos (Rema 111:1). One need not wash Mayim Acharonim on Shabbos, like Rema (Sof 170), for then we eat clean bread. The Pleisi (28:1) says that one must cover the blood immediately after Shechitah; if not he nullified the Mitzvah. Imrei Binah there asked, if so, why did our Gemara omit this? Megadim Chadashim - also Arugas ha'Bosem (31:3) proved from here like the Pri Megadim (Reish 28), that it need not be Tekef. Sho'el u'Meshiv (1:129) said that we did not list Semichus Chafifah li'Tvilah (Nidah 68a) for sometimes it is not possible (e.g. on Shabbos and Yom Tov), and always they are not so close - Chafifah is during the day and Tevilah is at night!
NOTE: According to Sho'el u'Meshiv, we could say that Kisuy ha'Dam was omitted, for it does not apply on Shabbos (even if Piku'ach Nefesh permits Shechitah - Yerushalmi Beitzah 1:3), However, I do not understand Sho'el u'Meshiv. The Rema (170:22) did not exempt from Mayim Acharonim. He said only that nowadays we are not careful about eating salt after eating, and drinking water after drinking! The Mechaber cannot hold like Sho'el u'Meshiv - the Mechaber obligates to be Somech Ge'ulah to Tefilah even on Shabbos! Also, why should we omit matters that apply even on Shabbos? (PF)
Daf Al ha'Daft citing Charedim on the Yerushalmi: Berachah must be Tekef to Mayim Rishonim and to Mayim Acharonim. The Bavli brings it regarding Mayim Acharonim, and the Yerushalmi regarding Mayim Rishonim. Therefore it brings the verse "Se'u Yedeichem Kodesh u'Varachu Es Hash-m" (Tehilim 134:2). It does not apply to Mayim Acharonim, for the hands should be down! The Tur brings from the Rosh that one may not speak between Mayim Acharonim and Berachah. Maharshal permits Divrei Torah; Shulchan Aruch ha'Ari and the Bach forbid even Divrei Torah. The Shulchan Aruch did not mention this. The Kesef Mishneh wrote that Rashi and the Ramban permit speaking. Magen Avraham forbids speaking between Mayim Rishonim and eating, even to answer Amen. Leket Halachah (3 p.78) questioned this. We are stringent not to interrupt then (due to Safek, perhaps our Gemara discusses Mayim Rishonim), and there is an argument if one may say two or three words. Surely one should answer Amen!
What is considered Tekef?
Tosfos (Sotah 39a): It is within the time to walk 22 Amos (about 11 seconds). We learn from Asham Metzora. Its Shechitah is not Tekef to Semichah, for Semichah is in Sha'ar Nikanor, and Shechitah was by the Mizbe'ach, 22 Amos away. (NOTE: This assumes that one may walk as fast as normal while leading an animal! - PF) Rav Elyashiv - since the Gemara taught these together, the same Shi'ur applies between Netilah and Berachah. However, Semichus Ge'ulah to Tefilah is truly immediately - Toch Kedei Dibur, for we learn from the Semichus of "Yiheyu l'Ratzon" to "Ya'ancha Hash-m b'Yom Tzarah" (Tehilim 20:2). (NOTE: If the Shi'ur of Semichus Semichah to Shechitah does not apply to Semichus Ge'ulah to Tefilah, even though they were taught together, what is the source that it applies to Semichus Berachah to Netilah? - PF)
Rav Elyashiv: Magen Avraham (166:3) says that one may be lenient to walk up to 22 Amos, but not from place to place, even within 22 Amos. He learns from Zevachim 33a. The Havah Amina was that Shechitas Asham Metzora may be anywhere in the north, even next to Sha'ar Nikanor. It is not Tekef because it is in a different place. L'Halachah, we are stringent if he cannot see the first place. Oneg Yom Tov (18) says that the time begins after he finishes drying his hands, for one may not eat until then. However, this is only for one who poured less than a Revi'is on his hands the first time, for then the water became Tamei. Our custom is to pour a Revi'is, so there is no need to dry the hands (158:13)! We must rely on Maharshal, who requires drying in any case, lest he wet the bread and make it repulsive. Even though he is a lone opinion, we rely on him, for the first opinion in 166:1 is not concerned for a Hefsek between Netilas Yadayim and eating. (NOTE: Mishnah Berurah (46) says that the Bach and all the Acharonim agree with Maharshal! - PF)
Rav Elyashiv: Some explain that it need not be Tekef, just one may not engage in other matters beforehand. Shulchan Aruch (166:1, 179) brings both opinions (for Mayim Rishonim and Mayim Acharonim).
Why did Abaye say 'also we learned'? (This is the text in Ein Yakov.)
Ha'Kosev: These words imply that this is connected to blessing on smell. (NOTE: The end of the coming Mishnah teaches that the one who blesses Birkas ha'Mazon, he blesses on the incense. - PF) Just like smell is a fine matter of the heart, and its benefit is not felt until spirituality is internalized, so one who connects with a Chacham, or a total Tzadik like Yakov or Yosef, he does not initially feel the great benefit until he is constantly with him. Biglal is an expression of Gilgul and causing. It does not come immediately, only via subtle causes that are not sensed initially.
What is the meaning of 'Tekef to a Chacham'?
Rashi: Right after drawing him close and hosting him.
How does "va'Yevarcheni Hash-m Biglalecha" show that Tekef to a Chacham is Berachah?
Maharsha: Rashi (Bereishis 30:27) said that Lavan had sons only after Yakov came. Our Gemara implies that his flock was blessed - "Ki Me'at Asher Hayah Lecha Lefanai va'Yifrotz la'Rov va'Yvarech Hash-m Osecha l'Ragli" (ibid. 30). Ibn Ezra explains, you were blessed once my foot entered your house. We bring also "va'Yvarech Hash-m Es Beis ha'Mitzri Biglal Yosef", for also that was immediate - "me'Az Hifkid Oso b'Veiso... va'Yvarech Hash-m..."
Rav Elyashiv: Yakov said "va'Yvarech Hash-m Osecha l'Ragli" regarding property. The Gemara cites Lavan's words "va'Yevarcheni Hash-m Biglalecha", even though it is written later, for it applies also to having sons. (NOTE: I do not know how to resolve this. This is before Yakov's words! - PF) "Va'Yvarech Hash-m Es Beis ha'Mitzri Biglal Yosef" applies to money and grandeur. This applies also to one who benefits a Chacham.
Etz Yosef citing Semichus Chachamim: It says "Biglalecha" and not Ba'avurecha, like it says elsewhere "Lema'an Yitav Li Ba'avurech." Surely Biglalecha teaches immediately; it is an expression of Galgal, like "bi'Glal ha'Davar ha'Zeh", Galgal ha'Chozer.
How does "va'Yvarech Hash-m Es Beis ha'Mitzri Biglal Yosef" show that Tekef to a Chacham is Berachah?
Etz Yosef citing Semichus Chachamim #1: Also here, we learn from the word Biglal.
Etz Yosef citing Semichus Chachamim #2: "Bayis" is extra, to teach that once he entered his house, he was blessed.
THE KEVI'US Needed for A ZIMUN
What is the meaning of 'his Talmidim went after him'?
Rashi: They buried him in another city.
Why did they need to infer 'this is only if they reclined, but not if they sat'? The Reisha explicitly says, if they were sitting, everyone blesses for himself!
Tosfos: One might have thought that the Reisha discusses when they sat for a different reason; they did not intend to eat. However, if they intended to eat, sitting helps without reclining!
Why did they ask only about Birkas ha'Mazon, and not about Berachah Rishonah?
Tosfos: Indeed, the Mishnah applies to both of these. The case is, they began eating at different times.
Rav Elyashiv: When returning they were weak and needed to eat [so they did not wait for each other to begin together]. It is possible that just like the law of tearing applies to Talmidim (just like to Avelim), also the law of Havra'ah (the first meal after the burial, he does not eat his own food).
Why did Rav Ada reverse his cloak and tear again?
Rashi: What he had torn in the eulogy of Rav was in front; he reversed his garment so the tear was in back, and tore again, to show a new mourning - they need a ruling, and there is no one to rule for them!
Daf Al ha'Daf, citing R. Z. Sorotzkin's eulogy of R. Aharon Kotler: If a second Mes died, it suffices to tear another Tefach, or tear three Tefachim away from the first! Why did he reverse the garment to make a new tear? He wanted to show that when one's primary Rebbi or the Gedol ha'Dor dies, he is not assessed properly on the day of death or burial, when one is heated and tears. The eulogizers see only what is in front on that day. They do not see what is in back - the consequences of the loss in the future.
Presumably, Rav's Talmidim did not know the Beraisa (which says that sitting suffices). If they knew it, they would have answered like the elder! If so, why were they unsure if our Mishnah is precise or not?
Etz Yosef: There are contradictory inferences from the Reisha and Seifa of the Mishnah. The Reisha says, if they were sitting, everyone blesses for himself. This implies that anything more than sitting, e.g. they summonsed themselves to eat, this is Kevi'us, like reclining. The Seifa implies that only reclining suffices! This is Rashi's intent.