Which brochos may be responded to during Shema?

During the prakim of Shema and its brochos, a person may only answer Amen to the following brochos: Hakel Hakadosh, Shomeya Tefilah, the brochos of an oleh l’Torah (according to some), and the brochos of Birchas Kohanim. Answering Amen to any brocha is permitted bein haprakim. Some say that one may only answer to the brocha of Ahavah Rabba when he is between Ahavah Rabba and Shema.

סעיף ג וס"ק יח ו־כג; ביאורים ומוספים דרשו, 10 ,14 ו־15 ;וראה סימן נט, סעיף ד

Can one say the entire Modim D’rabonon when he is in the middle of Shema?

During the prakim of Shema and its brochos, one should answer Amen Yehei Shmei Rabba and Amen at the end of half-Kaddish. One should also respond to Kedusha and Modim D’rabonon. When responding to Kedusha, one should only say the pesukim of Kodosh and Boruch. The poskim disagree about whether one must remain quiet during the rest of Kedusha or whether he can continue davening. All agree that it is appropriate to remain quiet. When responding to Modim, one should only say the first three words. According to some Achronim, one who already responded to Kedusha and Borchu that day should not answer again if he is in the middle of the prakim. The poskim disagree about whether one should say a brocha over thunder and lightning if he experiences them during davening.

סעיף ג וס"ק יז, יח ו־כ; ביאורים ומוספים דרשו, 11

May a brocha be said over a tallis during Shema?

According to the Shulchon Aruch, a person who was unable to put on tallis and tefillin before davening may put them on with a brocha if he is bein haprakim. Once he has already started the last parsha of Shema, however, he should put them on without a brocha. Rema allows tefillin to be put on with a brocha in the middle of the parshios of Shema and the brocha of V’yatziv. Regarding a tallis, however, he says it should be put on, but without a brocha -- even bein haprakim.

סעיף ב, ס"ק יד, טו, טז ו־יט, וביה"ל ד"ה אם; ביאורים ומוספים דרשו, 12 ;וראה שם, 5

• Each of the parshiyos and brochos of Kriyas Shema are known as prakim, and the points between them are known as bein haprakim. Bein haprakim, one may greet a respectable person (e.g. an elderly person or talmid chochom).

• The halachos of greeting people while davening applied only in an era when it was more common to greet people (even during davening). At that time, neglecting to greet someone was insulting. The poskim say that since greeting people during davening is not socially accepted today and people no longer expect to be acknowledged that way, it is forbidden to greet people or return their greetings during davening.

• The poskim extensively discuss whether writing is the equivalent of speaking. One case which is subject to debate is whether a person can be yotzei sefiras haomer by writing down the count of the day. 

• May one go up for an aliyah in the middle of Kriyas Shema?

• May a Kohein go up to duchen during Shema?

• Can one interrupt in the middle of Vayomer during Ma’ariv?