Saying Barchu at the end of Davening?
Letter of the law: One may recite Barchu at the end of Davening for the sake of people who did not yet hear Barchu that day. Certainly, if one did not yet hear Barchu he may say Barchu on his own behalf at the end of Davening. If, however, everyone in the congregation has already heard Barchu, then it is not to be said. Some communities however are accustomed for the Chazan to recite Barchu every weekday after the last Kaddish [Derabanan of before Aleinu], even in the event that everyone in the congregation has already heard Barchu. However, on Shabbos and Yom Tov they do not recite Barchu after Davening [unless there is someone present who did not hear]. Practically, in a shul, in order to avoid dispute, one is not to [protest or] nullify this custom [being that people in a Shul are unlearned]. However in a Beis Midrash, in which case there is no worry of dispute, it is to be accustomed that the Chazan does not recite Barchu unless there is a person present who did not yet hear Barchu. [The above follows the revealed aspects of Torah. However according to Kaballa, the Chazan is to recite Barchu daily after Davening, even on Shabbos and Yom Tov. On the other hand, there are Poskim who discourage and even prohibit the reciting of Barchu, even during the week, and even for a person who did not yet hear Barchu. Practically, each community is to follow their custom, as explained next.]
Practical customs of communities: The Chabad custom is not to recite Barchu at the end of Davening during the week, [even if there is a person present who did not hear it]. However, on Friday night the Chabad custom is to recite Barchu before Aleinu in all cases, even if everyone was present for Maariv. In most other communities however, Barchu is recited during the week in the event that there is a person present who did not yet hear it. Furthermore, many Ashkenazi communities are accustomed to recite Barchu after Davening on all days that the Torah is not read. The Sephardi custom is to recite Barchu at the end of Davening by all times, even on Shabbos and Yom Tov. However, some Sephardi Poskim write that a Sephardi is to recite a blessing [such as on a drink] after saying barchu in order to fulfill his obligation according to all opinions. The Chassidic custom in Eretz Yisrael is like the Sephardim, to rrecite Barchu after every prayer. However in the Diaspora, the custom of Chassidic communities is not to recite Barchu after Davening. Some of these Chassidic communities however do recite it on Friday night, while others do not.
The Chabad custom is not to recite Barchu at the end of Davening during the week, even if there is a person present that did not hear it. However, on Friday night the Chabad custom is to recite Barchu before Aleinu in all cases, even if everyone was present for Maariv. Each community is to follow his custom in this matter.
Saying Barchu by a Chabad Minyan:
As stated above, the Chabad custom is not to say Barchu after Davening. Often it happens that a non-Lubavitcher is by a Chabad Minyan and desires to say Barchu and the question arises as to whether it is permitted for him to do so.
May one say Barchu by a Chabad Minyan/Shul: If one is Davening by a Chabad Minyan that does not say Barchu after Davening, he is not to say Barchu at the end of Davening even if he did not yet hear it. If it occurred that one said Barchu by a Chabad Minyan, he can be gently told in a private manner that the custom of Chabad is not to do so. One can explain to him the severity of breaking this custom and that there are Poskim who rule that it is forbidden to say Barchu unless a blessing is said afterwards. Practically, the Mara Diasra in each community is to give directives to his congregation in this regard.
Must the congregation answer to his Barchu? If it occurred that one said Barchu by the Minyan, the congregation is to answer to the Barchu “Baruch Hashem Hamevorach Leolam Vaed”.
If one is a Chazan Davening by a Minyan that says Barchu after Davening, is he to recite Barchu?
Yes. One is to follow the custom of the community in this regard.
 Admur 69:4
 Admur ibid; Rama 133:1; Darkei Moshe 69; Elya Raba ibid; Bach; Derisha
Other opinions: Some Poskim rule that one is not to recite Barchu at the end of Davening in any situation, even if there are people present that did not yet hear Barchu, unless there is someone in the Minyan who is still Davening and reciting Birchas Shema. [Beis Yosef 69 and 133, brought in Kaf Hachaim 133:1, that it is only said for those that did not yet Daven; So also rules: Beis Yehuda 30; Beis David 340; Elya Raba in name of Nachalas Tzvi and Tosafus Yom Tov; See Rav Poalim 4:8] The reason for this prohibition is because it makes the congregation appear like heretics, as the term Barchu means “Lets bless” and if the congregation does not bless afterwards it appears that they do not want to bless Hashem. [Beis Yosef ibid in name of Mahariy Abuhav] However, according to the previous Poskim, there is no issue with saying Barchu without having a blessing follow it, being that in any event the congregation answers “Barchu Es Hashem Hamevorach”. [see Darkei Moshe 69; Elya Raba ibid; Bach; Derisha; Admur 69:4]
 Conclusion of Admur ibid that in Beis Midrash one is not to do so; M”A 69:1; Rameh Puno 84
 Ketzos Hashulchan 24 footnote 36
 Admur ibid; Rama 133:1; Beis Yosef 133; Rivash 334
The reason: They recite Barchu each day after Davening in order to fulfill the obligation of those that delay coming to Shul, and have not yet heard Barchu. Now, even if it occurs that everyone in the congregation was present for the original Barchu, they are nevertheless not particular against saying Barchu. [Admur ibid]
 Admur ibid; Michaber and Rama 133:1; Rivash 334
The reason: Even those places which are accustomed to recite Barchu each weekday after Davening on behalf of the latecomers who did not hear Barchu, nevertheless on Shabbos and Yom Tov they may not recite Barchu being that everyone comes to Shul before Barchu. [Rama ibid; Rivash ibid]
 Admur ibid; M”A 69:1; Rameh Puno 84; M”B 69 Hakdama; Yad Efraim; Derech Hachaim
 Arizal in Shaar Hakavanos and Peir Eitz Chaim, brought in Shalmei Tzibur p. 10, Rav Poalim 4:8, Kaf Hachaim 133:1, Ketzos Hashulchan 24:10
The reason: Barchu is said a second time even for those who already heard Barchu in order to elevate the sparks. This is unlike the understanding of the Poskim who say it is only said on behalf of those that did not hear Barchu. In truth every person must hear two Barchus, one before Shema and one at the end of Davening. [Rav Poalim ibid in name of Minchas Ahron p. 179]
 See “Other Opinions” above which forbid reciting Barchu unless there is someone remaining who will Daven afterwards. See also Darkei Chaim Veshalom 121 who stated “The Kedusha and Barchu of individuals said who Daven in private do not become elevated above”
 Igros Kodesh 10:296 [published in Shulchan Menachem 1:94] negates the saying of Barchu daily after the weekday Davening in all places, including Eretz Yisrael, based on Admur in the Siddur who omits this Barchu, and based on Minhag Beis Harav of which “We have never heard of this Barchu being said.” This letter however does not clearly negate the recital of Barchu by an individual who did not hear it. Nonetheless, the practical Chabad custom is not to recite Barchu at the end of Davening in any circumstance, even if one did not hear Barchu. [So is the widespread custom and so testified Harav Leibal Groner]
The reason: Perhaps the reason we do not say Barchu after Davening is because a) We do not accept the Kabbalistic reason during the week and b) we suspect for the opinion of the Beis Yosef which prohibits its recital of Barchu unless it is followed by a blessing. Alternatively, the reason is not because we suspect for the Beis Yosef but because of a general custom not to recite Kedusha or Barchu outside of the Minyan, as discouraged by Darkei Chaim Veshalom ibid. The practical ramification between the reasons is regarding if in a Chabad Minyan one may allow others to say Barchu if they came late. According to the Beis Yosef he may not say it unless some says a blessing. However according to the alternative reason, there is no loss involved in allowing him to say it.
 Siddur Admur; Igros Kodesh 10:296; Minchas Elazar 4:71; Likkutei Maharich Arvis Shel Shabbos
The reason: As according to the Arizal one is to recite Barchu on Friday night a second time. [See Peir Eitz Chaim Shabbos 14; Shaar Hakavanos Leil Shabbos 72; See Igros Kodesh ibid; Minchas Elazar ibid; Siddur Rav Raskin footnote 95]
 Luach Eretz Yisrael and Eretz Yisrael 1; Chazon Ish; Piskeiy Teshuvos 133:1 footnote 2
 Machazik Bracha 286:4 [brought in Shaareiy Teshuvah 286:5] “Custom of Eretz Yisrael and Egypt”; Mamar Mordechai [custom of his community; Shalmei Tzibur p. 212 “custom of Kushta”; Chesed Lealafim 133:22 “so is the correct custom”; Ruach Chaim “So is custom”; Yafe Laleiv; Rav Poalim 4:8 “So is custom in our communities, in contrary to the ruling of Maran”; Kaf Hachaim 133:1
 Or Letziyon 2:5-15
 Ketzos Hashulchan 24:36; Piskeiy Teshuvos ibid
 Minchas Elazar 4:71; Shulchan Hatahor 133:1; Likkutei Maharich Arvis Shel Shabbos; Piskeiy Teshuvos ibid
 Minchas Elazar ibid; Likkutei Maharich ibid
 Shulchan Hatahor ibid based on Baal Shem Tov
 See Piskeiy Teshuvos 133:1
The reason: He is not to do so, as it negates the Chabad custom, and according to some Poskim makes the congregation appear like heretics who do not want to recite a blessing afterwards.
 See Other Poskim in previous footnotes
 The reason: As otherwise even according to the Rama the congregation would be considered like one who does not desire to bless Hashem, as explained in Elya Raba ibid
 Piskeiy Teshuvos 133:1; See Admur 69:4 that one is not to change the custom in a Shul due to Mahclokes and see Igros Kodesh ibid