Barchu of Birchas Hatorah:
One is to recite Barchu prior to beginning the blessings over the Torah. The saying of Barchu serves as an introduction towards the blessing of “Asher Bachar Banu”, and is part of the blessing over the Torah that was instituted to be recited by the Oleh. It is said as an introduction in order to remind the congregation that they too are obligated in the reading of the Torah, and they should hence consent to his blessing and reading.
Out loud: One is to say Barchu and the blessings out loud. One who says it quietly is making a mistake. It is to be said loud enough for the congregation to hear and answer “Baruch Hashem Hamevorach Leolam Vaed”.
If the congregation did not hear: If the congregation did not hear the person saying Barchu, then if they heard the Chazzan answering in return, they are not to recite it with him but are to answer Amen to the Chazan’s Baruch.
If one forgot to say Barchu prior to the blessing of Asher Bachar Banu, is he to say it afterwards?
If an interval was made between Barchu and the blessing of Asher Bachar Banu, is one to repeat Barchu?
 Michaber 139/6
 Rav Poalim 4/8
 Raavan [Even Haezer] 73; Radbaz 1/572; Piskeiy Teshuvos 139/12
 Michaber ibid; Tur; Hagahos Maimanis Tefila 12
 Rama ibid; Tur ibid
 Rav Poalim 4/8; Beir Moshe 4/18
 The reason: Although doing so is not an interval, nevertheless it should not be said as the institution of the Sages was to recite it as an introduction to a blessing. Furthermore, according to some Poskim it is forbidden to say Barchu unless one says a blessing afterwards, as it makes the congregation appear like heretics. [Michaber 69; Beis Yehuda 30; Beis David 340; Elya Raba in name of Nachalas Tzvi and Tosafus Yom Tov] Accordingly, one may not say Barchu after the blessing, as there is no other blessing being said after it. [Rav Poalim ibid] However according to other 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”. [Darkei Moshe 69; Elya Raba ibid; Bach; Derisha; opinion of Admur 69/4] Accordingly, it would be permitted to recite Barchu after the blessing. [See Rav Poalim ibid] Nonetheless, it is best not to do so, as perhaps the institution was to say so only before the blessing, as stated Rav Poalim ibid. Likewise, the Chabad custom which does not recite Barchu after Davening leans towards the ruling of the Michaber ibid.
 Beis Yehuda 30; Emes Leyaakov 70; Chida in Ledavid Emes; Rav Poalim 4/8