Gemara

(Rav Chananel): Three groups of angels sing. One says "Kadosh". The next responds "Kadosh". The third responds "Kadosh Hash-m Tzevakos."

Question (Beraisa): Yisrael are dearer to Hash-m than the angels. Yisrael say Hash-m's Name after only two words - "Shma Yisrael, Hash-m... ";

Angels say His Name only after three words - "Kadosh, Kadosh, Kadosh, Hash-m Tzevakos."

Correction (Rav Chananel): Rather, one group of angels says "Kadosh", the next responds "Kadosh, Kadosh", and the third responds "Kadosh, Kadosh, Kadosh, Hash-m Tzevakos."

Question: Also angels say His Name after two words - "Baruch Kevod Hash-m mi'Mekomo"!

Answer #1: The Ofanim say that, but not the regular `angels.

Answer #2: Once angels have permission to say His Name (after saying "Kadosh, Kadosh, Kadosh"), they no longer need to say three words before it.

Megilah 23b (Mishnah): The following require at least 10 men:

To be Pores Al Shma (to say Kaddish, Borechu, and the first Berachah before Kri'as Shma);

Chazaras ha'Shatz (the Shali'ach Tzibur's repetition of Shemoneh Esre)...

(R. Chiya bar Aba): "V'Nikdashti b'Soch Benei Yisrael" teaches that matters of Kedushah require 10.

Rishonim

Rambam (Hilchos Tefilah 7:17): One skips the Kedushah in the first Berachah (before Kri'as Shma), for an individual does not say Kedushah.

Rosh (Megilah 3:7 DH Gemara): Any Devar shebi'Kedushah is said only with 10. An individual says Kedushas Yotzer, for it is mere Sipur Devarim, i.e. telling how servants above proclaim Hash-m's Kedushah (the person himself does not declare this), just like one may read the verses of Kedushah in Yeshayah. The Kedushah in Shemoneh Esre, in which we say 'Nekadesh (we will be Mekadesh)', requires 10.

Talmidei R. Yonah (Berachos 13a DH v'Nikdashti): Meforshim argue about whether 10 are needed for Kedushas Yotzer and Kedushas u'Va l'Tziyon. Some say that these are included in 'any Devar shebi'Kedushah is said only with 10.' When he reaches b'Safah Berurah, he skips the Kedushah. Chachamim of France and some Ge'onim say that an individual says Kedushah. Devar shebi'Kedushah requires 10 only when we say 'Nakdishach' and similar places in which we sanctify Hash-m. In Kedushas Yotzer we are not Mekadesh Hash-m. We merely mention the Kedushah that His servants say. The same applies to Kedushas u'Va l'Tziyon. It is mere verses. Kri'as Shma is the ultimate Devar shebi'Kedushah, for it has Ol Malchus Shomayim, yet an individual says it. 'Every Devar shebi'Kedushah' refers to whatever was enacted to say it amidst 10 due to Kedushah, e.g. Nakdishach. Kedushas Yotzer was not enacted to say amidst 10. Kedushas Yotzer is found in the text of what an individual says, but Nakdishach is not. This implies that only Nakdishach must be said amidst 10.

Talmidei R. Yonah (13b DH v'Yesh): Some disagree. In Megilah, we require 10 for Pores Al Shma, i.e. due to Kaddish. If they said Kaddish and Borchu and some left, they may finish. If an individual says Kedushah, what is the Chidush that they may finish?! Rather, Kedushas Yotzer requires 10. My Rebbi (R. Yonah) disagreed. If so, why didn't they use the Mishnah to challenge the opinion that an individual says Kedushah? Rather, Pores Al Shma is like the Rambam says. It is for people in the fields who cannot come to the Beis ha'Keneses. The Shali'ach Tzibur exempts them. This is only with 10.

Ran (Megilah 13a DH Masnisin): When one is Pores Al Shma, after Birkas Yotzer Ohr he begins Shemoneh Esre aloud. Why did the Mishnah teach that also the latter requires 10? The Yerushalmi says that if they began Pores Al Shma with 10 and some left, they finish, but they may not begin Shemoneh Esre aloud without 10.

Ran (13b DH v'Sham'inan): We learn from our Mishnah that an individual does not say Kedushas Yotzer. He says Seder Kedushah in u'Va l'Tziyon, for it is a mere Seder (arrangement) of verses.

Poskim

Shulchan Aruch (OC 59:3): Some say that an individual says the Kedushah in Birkas Yotzer (ha'Me'oros), for it mere Sipur Devarim.

Beis Yosef (DH Kedushah): The Rashba (Teshuvah 1:7) said that in a Teshuvah, the Rambam said that an individual says it. Also R. Yerucham and Mahari Avuhav said that the Rambam's son testified to this. He retracted from what he wrote in the Mishnah Torah. The Kolbo (8) says that since he said so only in a Teshuvah, but not in the Mishnah Torah, he holds that this is the Halachah, but we do not publicly rule like this. Orchos Chayim says that the Rambam's son testified that he retracted about how we openly rule. We rely on this.

Shulchan Aruch (ibid.): Some say that an individual omits it.

Beis Yosef (DH b'Perek): R. Yerucham says like the Ran, that an individual does not say Kedushas Yotzer. Ha'Manhig says 'an individual says "...b'Safah Berurah uv'Ne'imah. L'Kel Baruch Ne'imos Yitenu...", but not "Kadosh..." or "Baruch..." Also R. Natrunai Ga'on says so. Some say "Onim b'Eimah v'Omrim b'Yirah Kadosh u'Varuch. L'Kel Baruch..." This is wrong.' The Agur and Shibolei ha'Leket say that R. Eliezer of Virona had a similar text. R. Baruch disapproved, for the group of angels that says Kadosh does not say Baruch, like it says in Chulin. Rather, a person says "Onim b'Yirah v'Omrim Kadosh veha'Ofanim... Meshabchim v'Omrim Baruch." One does not complete the verses. He then begins l'Kel Baruch..." This is primary.

Gra (DH Yesh): Megilah 23b requires 10 for Pores Al Shma. Rashi (DH Ein Porsin) says that this is to say Kaddish, Borchu and Birkas Yotzer. It seems that we require 10 for Birkas Yotzer due to the Kedushah in it! The Ran says so. The Beis Yosef and Darchei Moshe (Sof Siman 69) sensed this; what they wrote is difficult. Also the Rambam and Ge'onim said so. R. Yonah brought this proof, but he also rejected the proof. The first opinion supported itself from Maseches Sofrim (16:9/12). It says that a minor who cannot be Pores Al Shma cannot say Kedushas Yotzer alone, but he may answer in a Tzibur. An adult can be Pores Al Shma or say Kadosh, since it is in Seder. However, in Kedushah of Shemoneh Esre we say Nakdishach, and it is improper to say so without 10. Really, this connotes oppositely! If we say that an adult is Pores Al Shma, there must be 10. If so, why does it say 'since (it is in Seder). However (Nakdishach... requires 10)'? Rather, it means that even though six who did not yet hear (Kedushah) suffice for Pores Al Shma, Kedushah of Shemoneh Esre requires 10 who did not yet hear. Rabanan in Eretz Yisrael say that seven suffice. A minor cannot be Pores Al Shma, therefore he can say Kedushah only b'Tzibur. An adult can be Pores Al Shma, so he can say amidst six or seven, since it is in the Seder of Pores Al Shma. This does not apply to Kedushah of Shemoneh Esre. The Zohar explicitly says so. The Beis Yosef says so. The Darchei Moshe is not concerned for the Zohar, since it is explicitly unlike Maseches Sofrim. I explained that also Maseches Sofrim holds that an individual does not say Kedushas Yotzer. Early Chachamim enacted to say Beraisos in place of Kedushah, for they hold that it requires 10. There is no reason to enact this according to the first opinion.

Mishnah Berurah (10): The Pri Chodosh says that even if one prays by himself because he came late to the Beis ha'Keneses, since there is a Tzibur, all permit saying it even quietly.

Kaf ha'Chayim (21): Ma'amar Mordechai says that all the Poskim disagree. It is like other Devarim shebi'Kedushah. If one came late, he cannot say Kaddish and Borchu just because 10 are there. The same applies to Kedushas Yotzer. The Mechaber connotes like this. For Kaddish and Borchu, as long as there are 10, even if three or four did not yet reach Kedushah, this is considered b'Tzibur. The same applies to Kedushas Yotzer and Kedushas u'Va l'Tziyon. For Kedushah of Chazaras ha'Shatz, 10 must answer, for nine (excluding the Shali'ach Tzibur) must listen to the Berachos.

Beis Yosef (DH v'Chasav): The Tur brought from Maseches Sofrim that an individual says Kedushas Yotzer. Mahari Avuhav says that he omitted that he must be at least 13 years old.

Mishnah Berurah (12): It is good to say Kedushas Yotzer while sitting, if possible.

Kaf ha'Chayim (20): Also Kedushas u'Va l'Tziyon should be said sitting.

Keser Rosh (27, in Sidur ha'Gra p.561): One does not pause between "Kadosh" and "Hash-m Tzevakos", for one group of angels says Kadosh" and "Hash-m Tzevakos

Note: The Gemara concluded that the third group says "Kadosh Kadosh Kadosh Hash-m Tzevakos." (It is difficult to say that Answer #1 holds that the Ofanim say Kadosh Hash-m Tzevakos, so we need not alter Rav Chananel's teaching. R. Baruch explicitly says unlike this.) Perhaps the Gra means that one should not pause from the first Kadosh until Hash-m Tzevakos.

Shulchan Aruch (ibid.): One should be concerned for their opinion, and say it with the tune and notes of one who reads Tanach.

Mishnah Berurah (11): The Gra holds like the latter opinion. One should not deviate from the custom (see the Rema below), so an individual should say it with the tune for reading Tanach.

Kaf ha'Chayim (22): It is good to always say it with the tune of Tanach, so he will be used to this and not transgress when he prays alone or comes late and says it alone. The Ari Zal would say all verses in Tefilah according to the tune.

Kaf ha'Chayim (23): One should say also Kedushas u'Va l'Tziyon with the tune.

Rema: The custom is like the first opinion. An individual says it. When we answer Kedushah, we say it aloud.

Gra (6): This is from the Yerushalmi and Tosefta.

Mishnah Berurah (13): It should be said loudly only b'Tzibur. Eliyahu Rabah says that an individual says it quietly. Sha'arei Teshuvah permits even an individual to say it aloud.

Kaf ha'Chayim (25): One should not kiss the Tefilin while answering, for one must answer with great Kavanah and fear. Also, it is improper to do something else while sanctifying a great king, even though he does so to cherish the Mitzvah.

Shulchan Aruch (132:1): One must say the Kedushah in u'Va l'Tziyon with great Kavanah.

Gra (2): This is because it is supporting the world (Sotah 49a).

Rema: The law of whether an individual says it is the same as Kedushas Yotzer. An individual says the Targum in this Kedushah; two do not say it (together). One should not say it loudly.

Taz (1): The Zohar says that the Tzibur does not say anything in Arameic.

Mishnah Berurah (3): L'Chatchilah it is better to say it with the Tzibur. Therefore, if the Shali'ach Tzibur begins v'Atah Kadosh before one reached there, he says it with the Tzibur, and afterwards says the two Pesukim that he skipped.

Kaf ha'Chayim (8): The Magen Avraham says that if the Tzibur says this Kedushah before one prayed Shemoneh Esre, he should say it with them. However, the Ari Zal says that it must be said in order, after Ashrei and la'Menatze'ach. One can say it alone with the tune.

Mishnah Berurah (4): One who prays alone may say the Targum aloud.

Kaf ha'Chayim (9): The Ari Zal said it aloud, but he did not say it together with anyone else.