Every Dovar Shebikdusha needs ten men, e.g. Kaddish, K’dusha, Borchu, Krias Hatorah, Haftara, N’sias Kapayim, Chazoras Hashatz. (ShA1 – MB 2,5,6)
If there was no minyan for Pesukay D’zimra, as long as you have a minyan for the Kaddish following it, the Kaddish may be said. The same applies to the Kaddish at Maariv. (MB2)
If more than one person is saying Kaddish in unison and they are within toch k’day dibbur of each other you should respond only one omayn to both – either after the first one or the second. But if they are separated more than k’day dibbur of one another, you must respond to each one. (MB4)
You should respond to no less than the following seven kaddayshim daily:
After the Yishtabach of Pesukay D’zimra
Half Kaddish after Shacharis Shemoneh Esray and Birchos K’rias Shema.
After K’dushas Uva L’Tzion which includes “Tiskabayl tzelos’hone” for the Shemoneh Esray as well
After the end of pesukim of Olaynu
After Ashray of Mincha
After Mincha Shemoneh Esray
After Birchos Krias Shema of Maariv before Shemoneh Esray (MB5)
If you are the tenth man you may not leave the minyan in the middle of a section – even though the remaining men may complete the section without you. They may complete it as long as there are at least six remaining.(ShA2 – Rama2)
For example: if you joined to be the tenth man just for Kedusha, you must stay until after Kaddish Tiskabayl which is the end of a section that began with Chazoras Hashatz. (MB12)
Even if you begin Olaynu with 10, do not say Kaddish after it without 10. The same goes for Shir Hayichud, mizmorim, or Torah learning – you need a minyan for Kaddish that follows. (MB 20)
If 10 men began Shemoeh Esray together and four left, the remaining men may recite the Kaddish Sholaym afterwards. On Motzoay Shabbos, they can say the Half Kaddish, Seder Kedusha, and Kaddish Sholaym because it is all one unit with the Shemoneh Esray like by Shacharis. (MB 22)
Today, our minhag is to include a child holding a chumash to the minyan only for Borchu and for an obligatory Kaddish. Many Achronim are machmir not to include a child under bar mitzva in a minyan even in urgent circumstances. (MB24)
In certain cases, an onen can combine to make a minyan. An ovel always combines to make a minyan.(MB 23)
Once a boy is thirteen years old, he is put on a chazzaka that he has two pubic hairs for the purpose of combining for a minyan. But for any deoraisa obligation the chazzaka is insufficient. (Rama5 – MB31)
Does a sleeping man count for a minyan? For Krias Megillah – no. For Krias Hatorah and duchaning – probably not. For Tefilla and Benching – the poskim argue – it is best to wake him to the point that he is only dozing. Even if he is not needed for the minyan, you need to wake him so he can merit responding to the Kaddish. (MB 34,35)
A minyan should wait to say Kaddish for an individual who is still daavening him so he can have the merit as well. (ShA 7)
A boy born in Adar Rishon whose 13th year is a leap year, becomes bar mitzva in Adar Rishon. If his 13th year is a regular year, he becomes bar mitzva in Adar. If a boy is born in Adar of a regular year, and his 13th year is a leap year, he becomes bar mitzva in Adar Sheni because Adar Rishon is not the real Adar (that we read the Megillah in) – it’s only the leap month. (ShA 10 – MB 43,45)
A boy born on Rosh Chodesh Kislev in a year with only one day Rosh Chodesh, and on his 13th birthday there are two days of Rosh Chodesh – becomes bar mitzva on the first day. (MB 45)
If the tenth man is in the ezras noshim and he shows his face through a window in the mechitza, he combines to make the minyan. Doing that also helps for him to be considered daavening tefilla b’tzibbur. Nevertheless, it is better to go into the main shul because some hold that the ability to see each other is insufficient. (MB 52)
All 10 men must be in one place even if they do not see each other. If there is a mechitza (not just for tznius) dividing the minyan and they do not see each other, they don’t combine. Some are machmir even when they do see each other. (ShA 13 – MB 48,49)
Men that can see each other from two different buildings can combine to make a minyan if there is no other choice. (MB 57)
Wherever there are ten men daavening, the Shechina is present and no wall is able to separate between the Shechina and anyone who wants to combine with it. Therefore, even if you are in a different house you may respond when you hear their Kaddish or Kedusha. But for Borchu, answer only if there is no filth, idol, or idolater in between you and the minyan. (ShA 20 – MB 60,62,65)
If forming a minyan is important enough to release a slave (as Rabi Eliezer did) certainly it is important enough to go to the effort of gathering the men together. How great is the mitzvah of the one who gathers the minyan in a small community to make sure that Tomid is never nullified. (MB73)