Is it tefilah b’tzibur if one davens in a room next to a shul?

An individual who davens in a room adjacent to a shul with a minyan does not fulfill his obligation of tefilah b’tzibur. If, however, he is standing in a room which can only be entered through the room where the minyan is standing, he would fulfill the obligation. Some are lenient even if the room has other entrances.  

ס"ק נז (וביה"ל ד"ה שליח); ביאורים ומוספים דרשו, 73

Should one respond to Kedusha if he learning in an adjacent room?

A person standing next to a shul may respond to Kaddish and Kedusha even though he is not considered part of the minyan. The poskim disagree about whether he is obligated to respond or whether responding is optional since he is not part of the minyan. If he is learning or davening, he is exempt from responding. Some say that although he is exempt, he should answer to Kedusha, Borchu and Modim D’rabonon.

סעיף כ וס"ק ס-סה; ביאורים ומוספים דרשו, 75 ;וראה שם, 7

Can the tenth man leave town for the Yamim Noraim?

A person who lives in a city with only ten Jewish men may not leave for the Yamim Noraim unless he hires another person to take his place. Even if he is accustomed to leave every year, he must remain if he is needed for the minyan (e.g. if the number of residents dwindled). If, however, the residents generally leave for the Yamim Noraim, they cannot compel an individual to stay in town if they want to make their own minyan one year.

סעיף כא וביה"ל ד"ה עיר; ביאורים ומוספים דרשו, 82

• The ten members of a minyan must be in the same room. If there are in two different rooms, they are not counted together even if there is an open door between the rooms.

• Regarding the halochos of zimun, people in a different room can join if they can see one another. Some Rishonim draw a parallel to a minyan and allow people who see each other to be counted together for a minyan even if they are not in the same room. Shulchon Aruch rules according to this view, while other Achronim are stringent.

• If a dividing wall between two rooms breaks open, the space is regarded as one room and the people in both rooms can be counted together to make a minyan.

• Is it permissible to learn during Kaddish?

• May Kaddish be said quietly?

• Must the one saying Kaddish adopt the shul’s nusach?