What is the reason to say Nevarech?

Rav Elyashiv: A Mitzvah requires preparation.

When there are three and him, why does he say Barchu?

Rashi: There is a Zimun even without him.

How can the Mishnah say that 10 are the same as 10,000? Below it distinguishes if there are 100, 1,000 or 10,000!

Rashi: The Gemara will ask this. The Reisha is like R. Akiva, who does not distinguish once there are 10 or more.

What is the significance of 10, 100...?

Maharsha: Every 10th is Kodesh; it is the source and end of all numbers. The first Ma'aleh (step, or level) is 10; the second is 20... until 100, which gets a new name. When we reach 1,000, this returns to the Ma'alah of 1, 10 and 100, for it is 10 times 100. The first Tana (R. Akiva) holds that since 10 is the source of all numbers, we do not distinguish 10,000 from 10.

Does the text say Nevarech Elokeinu or lEi'lokeinu?

Tosfos citing Seder Rav Amram : It is Elokeinu. We find it with the prefix Lamed only regarding Shir and thanks - "Shiru la'Shem", "Hodu la'Shem", "Gadelu la'Shem Iti."

Why do we say Elokeinu in a Zimun, and in the Beis ha'Keneses, we say Barchu Es Hash-m?

Chashukei Chemed citing Tif'eres Yakov (on Mishnayos, Sof Perek 7): Perhaps we say Elokeinu in a Zimun¸ for it is 'hard' to finance people.

It seems that R. Yosi ha'Gelili agrees about Beis ha'Keneses. Why is Zimun different?

Tosfos: We do not distinguish in Beis ha'Keneses, for some enter and some leave, and [the Shali'ach Tzibur] is not aware. Birkas ha'Mazon, they are fixed together, and the Mezamen would not err. People do not leave until after Birkas ha'Mazon!

Chashukei Chemed: This implies that we should change the text in Beis ha'Keneses when there are 100, just we do not lest the Shali'ach Tzibur err. i.e. Tefilah amidst 100 is greater than Tefilah amidst 99 (even though regarding "b'Rav Am Hadras Melech", the difference is negligible). R. Akiva could agree to this, just he holds that we do not change the text even for Birkas ha'Mazon.

Maharsha: Birkas ha'Mazon is explicit in the Torah; the verse ("b'Makhelos...") discusses it.

How does R. Yosi ha'Gelili learn from the verse?

Maharsha: It could have said b'Kahal. Rather, b'Makhelos (plural) teaches that the Berachah is according to the size of the Kahal, i.e. new names acquired based on powers of 10.

Why did Shmuel say 'one should never exclude himself from the assemblage'?

Rashi: When there are four, even though he may say Barchu, it is better to say Nevarech, to include himself among those who bless.

Tosfos: The Yerushalmi asks that one who reads from the Torah and a Shali'ach Tzibur say Barchu!

Ha'Boneh: He said never - whether for evil or good, it looks like haughtiness. If it is evil, he shows that he is better than them. Moshe said "Lo Sa'asun k'Chol Asher Anachnu Osim Poh ha'Yom." Yeshayah said "ki 'Sdom Hayinu la'Amorah Diminu." If it is for good, like it says here - it looks like he tells them to bless, and he establishes himself to be at a high level, and does not humble himself in front of Him via a Berachah.