Mishna Berura Source Sheet 192:1 How (not) to Conduct a Zimmun -

רַבּוֹתַי, נְבָרֵךְ

Although this is not in the official zimmun script but as a vital setup. It's like saying, "Hey, my friends at the table, thanks for joining the lunch party! Now, let's gear up to shower Hashem with blessings through a zimmun!"

However, this statement isn't just a "pep" talk, it is to achieve the Kabbalsitic function of benching, as it is imperative to have a verbal preparation in order for the kedusha to descend.

This practice, highlighted in the Zohar, holds true irrespective of the scale of the mitzvah – no deed is too big or small. A noteworthy illustration of this principle can be traced back to the construction of the mishkan, the sacred dwelling place crafted by the Jewish people in the desert for Hashem. Even in this grand undertaking, the act of verbally dedicating oneself to the mitzvah played a pivotal role in invoking and channeling the kedusha that lies therein.

נְבָרֵךְ

The enactment of "zimmun" is a collective ritual wherein three or more individuals who have shared a bread meal join forces during a segment of the benching to amplify the reverence for Hashem's name.

After the "zimmun", individuals proceed with the standard benching practice.

המסבים עונים:

אמן

There's a disagreement in the Poskim whether the participants should answer "Amen" after the leader says this blessing.

On one hand, I would say the reason is because, after there is an opportunity for an Amen hanging in the air. However, this is not the justification to recite Amen, see Eliyahu Rabbah below for the reason why Amen would be appropriate to be said by the participants. See also Magen Avraham at length.

On the other hand, they just said that beracha in its entirety just before, so the need to answer Amen to the beracha would seem to be unnecessary, if they just said the beracha with their own mouths, the need to acknowledge the same thing said by someone else would seem to be unnecessary in order to show validation towards it.

Nevertheless, all Poskim agree that the when the leader repeats their blessing, he does not recite Amen אמן, since he is about to repeat the exact beracha, and it precludes the need for an Amen.

ברוך הוא וברוך שמו

There is controversy whether this should be said by the leader at this point. Mishna Berura says that the accepted minhag is to say it.

Darchei Moshe writes (brought in Be'er Heitev) that this phrase serves as a "separation" between the zimmun procedure and the actual benching.

(בארבע: ברכו שֶׁאָכַלְנוּ מִשֶּׁלוֹ)

The mishna in Berachos brings many variations of the opening phrase of zimmun, and this is one of them. However, our minhag is not to vary the opening phrase of the zimmun, regardless if there are 3, 10, or more people at the meal.

We see that the term "Barchu" finds its appropriate usage only when a 3-person-zimmun could have taken place even without the presence of an additional fourth. In recognition of the fact that a sanctification could have been made even if he wasn't there, he uses the Barchu term.

If a person used Barchu when there were only three people total, there is a dispute whether the zimmun is valid.

לאֱלֹהֵינוּ

One should not put a ל before Elokeinu because in most pesukim about berachos, a lamed doesn't appear before the name Elokeinu. Being that zimmun is a type of beracha, we want to follow the lead on how the Torah describes Hashem in pesukim that discuss berachos.*

I'd like to add that the commentators on that passage explain that it pertains to what the collective of Klal Yisrael will express to non-Jews in the ultimate future. However, it's noteworthy that this concept aligns with the idea of zimmun.

The Siddur commentaries (see Hakdama to Birkas HaMAzon Iyun Tefilla) suggest that the genesis of the zimmun concept traces back to Avraham Avinu, who, in welcoming non-Jewish guests into his home, imparted knowledge about the existence of Hashem.

Thus, the use of similar terminology in a verse discussing influencing and interacting with non-Jews serves as a fitting parallel and reference point, emphasizing the shared theme of educating others on how to bless Hashem in various aspects of life.

In the same vein of the connection of the genesis of zimmun from Avraham to the nusach of the zimmun, I'd like to add one more thing.

Another incorrect terminology to be used in zimmun is על המזון שאכלנו

Other Rishonim explain the reason the nusach is inappropriate for a different reason, because it connotes that you are thanking the food for feeding you, when in truth it is Hashem who orchestrates food to nourish, food itself has no power to nourish, so it is appropriate to bless Hashem, and not the food.

The emphasis people had, and sometimes still do have, on primarily thanking the host was a misconception that Avraham tirelessly tried to educate his guests about, as the Gemara in Sotah relates.

על המזון שאכלנו*

This incorrect nusach ends with an asterisk because there is an exception to this ruling, and this terminology can be used. The Shulchan Aruch says (seif 2) that if one is doing a zimmun with 10 people, where "Elokeinu" is mentioned, the phrase is clearly referring to blessing Hashem. However, this is not our minhag to switch nusachaoes.

למי שֶׁאָכַלְנוּ מִשֶּׁלוֹ:

Adding the word "let us bless to whom we ate from" is also an unacceptable terminology. By specifying a specific address - "to whom", it connotes that we have many different sources for getting sustenance, and at this particular meal we are blessing the particular individual gave us this meal, namely the host, which is inappropriate being that benching is foremost thanking Hashem. (This is not to say that we don't owe a debt of gratitude towards the host, nevertheless it doesn't belong in this portion of benching where the focus is on blessing Hashem)

וּמטוּבוֹ

By saying "from His goodness, it connotes that we are minimizing the gift of life that Hashem endows to us, that it is just a part of His kindness. We should see our gift of life as an expression of Hashem's goodness as grand!

חיים

This too is not appropriate, since it connotes that the person is blessing Hashem for life in general, but not his life. It is not proper to remove oneself from blessing Hashem for a goodness he, the one blessing, also receives from Hashem.