Speaking/Hefsek for the sake of Davening:
The subject of speaking [i.e. Hefsek/interval] during Davening carries many laws and details, regarding the cases in which it is permitted to be done. It is beyond the scope of this article to summarize all these detailed laws, and its focus is solely on the general subject of talking for the sake of Davening.
A. The general law of Hefsek for the sake of a Mitzvah:
Hefsek for the sake of a Mitzvah: It is forbidden to make an interval between Baruch Sheamar [and Yishtabach, and between Birchas Shema] and Shemoneh Esrei even for the sake of a Mitzvah [with exception to those cases explicitly recorded in the Poskim].
Between Yishtabach and Yotzer Or: Some Poskim rule that between Yishtabach and Yotzer Or, one may even initially speak for the sake of a Mitzvah. [However, other Poskim rule one may not speak for the sake of a Mitzvah even between Yishtabach and Yotzer Or.] Practically, the custom and final ruling follow the former opinion. [However, some Poskim rule that today the custom is to no longer make an interval in-between Yishtabach and Yotzer Or, even for the sake of a Mitzvah.]
B. Speaking [i.e. Hefsek] for the sake of the Davening:
Some Poskim rule that the above prohibition against making a Hefsek even for the sake of a Mitzvah only refers to a Mitzvah that does not involve the Davening. However, one may speak for the sake of Davening [such as in the examples to be explained] whether in Pesukei Dezimra or Birchas Shema. Other Poskim however rule one may not speak even for the sake of Davening, [with exception to the cases to be explained], and so is the ruling of Admur. Practically, in a time of need one may be lenient during Pesukei Dezimra, as will be explained.
It is forbidden to speak for the sake of a Mitzvah, unless one is between Yishtabach and Yozter Or, in which case some Poskim rule that one may be lenient. However, if the matter is for the sake of Davening, one may be lenient in Pesukei Dezimra.
May one ask someone to join the Minyan?
Yes. It is permitted to do so even if one is in Birchas Shema. However, one should only do so if he cannot communicate through writing [i.e. SMS messaging, whatsapp etc].
May one announce the page number for the congregants of the Minyan?
Some Poskim rule that one may do so between the Perakim of Pesukei Dezimra, however not in Birchas Shema. Initially, however, one is to prepare cards with the page numbers and raise them upon reaching the place, for the congregation to see. One may not announce the page numbers in Birchas Shema, even if it means that he will have to Daven in private at home. [Nonethelss, some Poskim are lenient even in such a case.]
May one announce that there are feces in the area and it is therefore forbidden to Daven?
May one correct the Baal Korei if he is in middle of Pesukei Dezimra?
Yes. [However, only if this is a correction that is due to a pronunciation which invalidates the words.]
If one remembered in middle of Davening that he did not recite Birchas Hatorah what is he to do?
Pesukei Dezimra: If one remembers in middle of Pesukei Dezimra, or between Yishtabach and Barchu, then he is to stop and recite all three blessings of Birchas Hatorah, including the verses of Birchas Kohanim.
Birchas Shema: If, however, he already began Birchas Shema, then he may no longer stop to say it. Some Poskim rule he is to intend not to fulfill his obligation with Ahavas Olam and then recite Birchas Hatorah after Davening. Others however rule that one is to specifically intend to fulfill his obligation with Ahavas Olam and is to then learn Torah immediately after Davening. Practically, one is to follow the latter opinion.
May one wear Tallis and Tefillin with a blessing in middle of Davening?
See our Sefer “The Laws of Tzitzis” chapter 1 Halacha 8, and our future Sefer on “The laws of Tefillin” where this matter is discussed in length.
 Admur 51:4 and 53:3; Rama 51:4; Levush 51:5
 For example, Mitzvos that will be lost if delayed, such as the blessing over thunder, may be said in Birchas Shema. [Admur 66:4; M”B 66:19]
 Admur 51:4; 53:3 [regarding blessing on Tallis]; 54:3; Michaber and Rama 54:1
 Tur in name of Seder Rav Amram Gaon; Kol Bo 4
 Rif; Rosh, brought in Kaf Hachaim 54:11; See Darkei Moshe 54:
 See Admur 51:4; 53:3 [regarding blessing on Tallis]; 54:3-4; Rama 51:4; 54:1
 Implication of Michaber 51:4; Aruch Hashulchan 54:4; Kaf Hachaim 54:11; Shulchan Hatahor 53:1; See M”A 54:2 regarding saying Shir Hamaalos between Yishtabach and Yotzer; Igros Kodesh 8:99; Piskeiy Teshuvos 54:3 in name of Darkei Moshe; Hefesk Betefila 2:10 footnote 15 [p. 39] based on M”B 53:7 who prohibits initially stopping for a Mitzvah between Yishtabach and Yotzer
 So rule regarding Yaleh Veyavo before Shemoneh Esrei of Maariv: Michaber 236/2 based on Rashba 293; Bach 236 [see Machatzis Hashekel ibid]; Levush Abudarham; M”A 236/1; M”B 236/7; 422/1; Derech Hachaim 33/81; See Peri Hasadeh 2:15; Hisorerus Teshuvah 4:4 regarding getting a Minyan
 The reason: As an interval which is done for the need of the prayer is not included in the prohibition against making a Hefsek. [Implication of Michaber ibid; Igros Moshe ibid regarding Pesukei Dezimra] Now, although sthe Rashba writes that it is allowed due to the fact that the Shemoneh Esrei of Maariv is voluntary [see M”A ibid in name of Rashba] nonetheless, this is not the main reason in the Rashba, and the main reason is as explained above, that the allowance is due to that it is being done for the sake of the prayer. [Machatzis Hashekel ibid that Bach argues and learns the main reason of Rashba is due to that it is for the need of prayer]
 So rule regarding Yaleh Veyavo: Siddur Admur; Sefer Haminhagim p. 69 [English]; Rashal brought in M”A 236:1; Kaf Hachaim 236/16; Ketzos Hashulchan 27/5; Igros Moshe 1:22
 The reason: As the main reason of the Rashba ibid for permitted announcing Yaaleh Veyavo is due to that Shemoneh Esrei is a voluntary prayer. [M”A ibid in name of Rashba; Rashal ibid, explained in Machatzis Hashekel; Igros Moshe 1:22]
 Igros Moshe 1:22
The reason: Although some Poskim learn that the allowance by Maariv is only due to the fact that the Shemoneh Esrei of Maariv is voluntary [see M”A ibid in name of Rashba; Rashal and Sidur Admur, brought in previous footnote; However, see Machatzis Hashekel ibid that Bach argues and learns the main reason of Rashba is due to that it is for the need of prayer] nevertheless, Pesukei Dezimra is more lenient in this regard, as the prohibition of Hefsek is due to the Hefsek in middle of the blessings, and just like one may make a Hefsek after a blessing, before the Mitzvah, for the sake of the Mitzvah, so too here. [Igros Moshe ibid]
 Hisorerus Teshuvah 4:4; Peri Hasadeh 2:15
 The reason: As it is permitted to even transgress a Biblcial command of freeing a slave for the sake of having a Minyan [see Admur 90:17], thus certainly one may transgress the laws of Hefsek for the sake of having a Minyan. Likewise, Bein Haperakim is no worse than than asking Shalom due to Kavod. [Hisorerus Teshuvah ibid]
 Hisorerus Teshuvah ibid
 Igros Moshe 1:22
 The reason: Although some Poskim learn that the allowance by Maariv is only due to the fact that the Shemoneh Esrei of Maariv is voluntary [see M”A ibid in name of Rashba; Rashal and Sidur Admur, brought in previous footnote; However, see Machatzis Hashekel ibid that Bach argues and learns the main reason of Rashba is due to that it is for the need of prayer] nevertheless, Pesukei Dezimra is more lenient in this regard, as the prohibition of Hefsek is due to the Hefsek in middle of the blessings, and just like one may make a Hefsek after a blessing, before the Mitzvah, for the sake of the Mitzvah, so too here. [Igros Moshe ibid]
 Igros Moshe ibid based on the stringent opinion above
 All Poskim in 1st Q&A who permit announcing Yaaleh Veyavo; as well as Hisorerus Teshuvah ibid
 Piskeiy Teshuvos 51:7
 Lev Chaim 3:5
 See Michaber 142:1
 M”B 51:10; as there are opinions who say it is forbidden to recite the verses in Pesukei Dezimra prior to Birchas Hatorah.
 M”B 51:10
 Peri Megadim 52; However, there are Poskim who argue on this advice, and state it does not help even if one has this in mind. [See Biur Halacha 52 “Umikol Makom”; Tehila Ledavid 47:6]
 M”B 52:9; Biur Halacha “Umikol Makom”
 As explains Biur Halacha ibid and Tehila Ledavid ibid the reasons not to rely on the advice of the Peri Megadim, and so is also implied from Admur in 47:6
May one announce to the congregation, during Pesukei D’zimra, that sof zman krias Shema is approaching and whoever did not yet say Krias Shema should say it now before it will be too late?