the source for a Zimun
What is the meaning of ate like one'?
Rav Elyashiv: They fixed to eat together, or they finished together.
What is being Mezamen?
Rashi: They join together to bless in the plural, e.g. Nevarech.
What is the question 'what is the source [for our Mishnah]?'
Rashi: What is the source that three may bless together? In both answers, we find that [at least] two join with one - "Gadlu la'Shem Iti", or one tells two "Havu Godel."
Etz Yosef citing Mayan ha'Berachos: Why did the Gemara cite also "u'Neromemah Shemo Yachdav"? We already learn three from "Gadlu la'Shem"! It was to teach the text, that the Mezamen must say Nevarech, to include himself (also I will bless). From Gadlu la'Shem Iti, we would think that he may say Barchu. The verse did not say Negadlah, lest we think that two suffice for a Zimun. Also according to R. Avahu, who learns from "Havu Godel l'Eilokeinu", the Mezamen must include himself; Moshe said first "Ki Shem Hash-m Ekra."
NOTE: We can say also according to R. Asi, "Gadlu la'Shem Iti" shows that also I will bless! (PF)
Is the Chiyuv to be Mezamen mid'Oraisa or mid'Rabanan?
Rav Elyashiv: The Tur (Shemoneh Esre) brings from the Ra'avad that it is mid'Oraisa. Most Acharonim hold that it is mid'Rabanan; the verses are mere Asmachtos. All agree that if the people did not eat to satiation, it is mid'Rabanan, for mid'Oraisa they need not bless.
Megadim Chadashim: Sha'ar ha'Tziyun (199:19) says that most Poskim hold that it is mid'Rabanan; Chazon Ish (OC 31:1) asked 'whom are these majority of Poskim'?
Why is it forbidden to answer Amen louder than the Mevarech?
Rav Elyashiv: This is only when the Mevarech is Motzi people; it is due to honor of the Tzibur. (After this, the Gemara forbids the translator to be louder than the Korei, for he suppresses the Korei's voice.) Since it is only when he is Motzi, it does not apply to Kaddish or Zimun. However, the Rambam (Hilchos Talmud Torah 4:3) applies this even to a Rebbi teaching Talmidim; the translator may not be louder due to the Rebbi's honor.
Rav Elyashiv: Some Sheluchei Tzibur err and are Makri (say the words of Birkas Kohanim for the Kohanim to repeats) softly, lest the Kohanim say it lower. The law here (they should be equally loud) does not apply, for no one answers! The Shali'ach Tzibur is Makri lest the Kohanim err.
May one answer Amen in a lower voice than the one who blessed?
Etz Yosef: No. He should answer in the same voice, like it says "Gadlu la'Shem Iti u'Neromemah Shemo Yachdav." "Yachdav" implies equally.
What is the proof from "Moshe Yedaber"? It does not say that he translated, nor that he did not speak louder than Hash-m!
Tosfos citing the Rif (Alfasi): Presumably, Moshe spoke as loud as he could, so all of Yisrael could hear. Why did Hash-m speak as loud as Moshe? Only Moshe needed to hear Him! Rather, it is because Moshe was forbidden to speak louder than Hash-m.
Maharsha: Really, Moshe spoke in Leshon ha'Kodesh. Not everyone understood this, so Hash-m spoke in all 70 languages (Shabbos 88b) - He translated for every [Goy] according to the language that he understands. (NOTE: This is unlike a translator, who translates for the same people who hear what the Korei reads from the Sefer! - PF)
Iyun Yakov: Surely Hash-m was Korei to Moshe, and Moshe translated - "Ho'il Moshe Be'er Es ha'Torah" (Devarim 1:5) - in 70 languages (Rashi there, from Tanchuma 2). Just like the translator may not speak louder than the Korei, the Korei may not speak louder than the translator. So rule the Rambam (Hilchos Tefilah 12) and the Tur (OC 145). This is why Hash-m spoke as loud as Moshe.
Megadim Chadashim: Here we discuss the time of Matan Torah - "Moshe Yedaber veha'Elokim..." Moshe translated it into 70 languages afterwards!
Etz Yosef citing Mayan ha'Berachos: The Gemara taught that the translator may not be louder, and we know that the Korei may not be louder, for this is clear from the verse. Had the Gemara taught the latter, it would not be clear whether the former is true.