Saying the blessings over the Torah out loud:[1]

One is to say Barchu and the blessings out loud. One who says it quietly is making a mistake.[2] [One who says it quietly is consider to be stealing the Mitzvos from the public.[3]] It is to be said loud enough for the congregation to hear and answer “Baruch Hashem Hamevorach Leolam Vaed” [and Amen[4]].[5] [Initially, the blessings are to be said loud enough for the entire congregation to hear.[6]]

Bedieved if said quietly: Some Poskim[7] rule he must repeat the blessings aloud if it was said quietly.[8] [Other Poskim[9] rule it does not have to be repeated. Practically, the blessings are not to be repeated.[10] However Barchu is seemingly to be repeated.[11] From here we learn how great of an obligation it is to say the blessings out loud, as otherwise, some opinions invalidate the blessing.[12]]

Answering Amen if one did not hear the blessings:^[13] If one did not hear the person saying the blessing, he may nevertheless still answer Amen together with the congregation.^[14]  Furthermore, he is obligated to do so.^[15] This applies even if one intended to fulfill his 100 blessings with this blessing.[16] Nevertheless, one does not fulfill his obligation of Meiah Brachos with such a blessing unless he heard the blessing from the person saying it.^[17]

Answering Baruch if one did not hear the Barchu:[18] If the congregation [i.e. nine men] 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, however nine people heard the Chazan say Barchu and are answering Barchu, an individual that did not hear the Chazan may join in and answer Barchu together with the congregation.[19] Due to this, the Oleh is to be warned to say Barchu aloud so at leats nine people can hear. Those that don’t do so cause the congregation to sin when they answer Barchu instead of Amen.[20] Bar Mitzvah boys, and those who are weak or sick are especially to be told to say it aloud, and have nine people gather near them to hear the Barchu.[21]]

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[1] Michaber 139/6; Hagahos Maimanis Tefila 12; Mahariy; Rabbeinu Yona

Other opinions: Some Poskim rule the blessings over the Torah [besides Barchu] may to be said quietly. [Mahariy Abuhav in explanation of Tur 139 in name of Rav Yechiel, brought in Beis Yosef 139 and P”M 139 A”A 10]

[2] The reason:  As the blessings may only be said in the presence of ten people listening, and when said quietly it is as if he is saying it in private without a Minyan. The same applies to Kaddish. [M”A 139/10; Beis Yosef; Mahariy] Alternatively, it is said aloud in order so the congregation answer Amen. [M”B 139/23]

[3] Sefer Chassidim 254; Kneses Hagedola; Yefie Laleiv 139/8; Kaf Hachaim 139/37

[4] M”B 139/23

[5] Rama ibid; Tur ibid

[6] Kaf Hachaim 139/38

The reason: This is to suspect for the reason that it is said aloud in order to fulfill the obligation of the congregation. However according to the reason that the blessing requires a Minyan, then it is not necessary to say it loud enough for the congregation to hear, so long as ten people can hear him. [Kaf Hachaim ibid] Now, although Admur rules it is not necessary to be Yotzei the blessings of Kerias Hatorah as it is the obligation of the Oleh, nevertheless, perhaps there are people present who desire to be Yotzei their 100 blessings, and hence it should be said out loud for everyone to hear.

[7] Opinion in Michaber ibid; Rabbeinu Yonah brought in Beis Yosef 139; One way of understanding Rosh brought in Tur 339

[8] The reason: In order so the congregation fulfill their obligation with the blessing. [Rabbeinu Yonah ibid, brought in Beis Yosef 139] Alternatively, it is because the blessings must be said in public. [Rabbeinu Yonah ibid; M”A ibid] Alternatively, the reason is in order for the congregation to hear and answer “Baruch Hashem Hamevorach Leolam Vaed” [Rama ibid] This implies that according to the Rama only Barchu must be repeated and not the other blessings. [Elya Raba 139/9; M”B 139/25 and Biur Halacha “Vehabrachos”; Kaf Hachaim 139/41] However, others explain the Rama ibid to mean that since the blessings were instituted to be said in public, therefore they must be repeated. [P”M 139 A”A 10 in explanation of Rama ibid]

[9] Mahariy Abuhav in explanation of Tur 139 in name of Rav Yechiel, brought in Beis Yosef 139 and P”M 139 A”A 10

Does this opinion argue also on Barchu? Seemingly they only argue regarding the blessings and do not argue regarding Barchu, and so rules Elya Raba 139/9; M”B 139/25 and Biur Halacha “Vehabrachos”; Rama ibid. However, see Kaf Hachaim 139/41 who learns from the fact that this ruling of Michaber was omitted from many Achronim, that even Barchu is not required to be repeated. So rules also Piskeiy Teshuvos 139/13

[10] Elya Raba 139/9; Shaareiy Efraim 4/7; M”B 139/25 and Biur Halacha ibid “Vehabrachos” that Safek Brachos Lihakel; Kaf Hachaim 139/38 that so is implication of many Poskim who omit the above ruling of Michaber ibid, such as: Levush 139; Chida in Ledavid Emes 6/60; Chayeh Adam 31/12; Derech Hachaim 4

[11] So rules: Rama ibid; Elya Raba 139/9, M”B 139/25; However, see Kaf Hachaim 139/41 who learns from the fact that this ruling of Michaber was omitted from many Achronim, that even Barchu is not required to be repeated. So rules also Piskeiy Teshuvos 139/13

[12] Biur Halacha ibid

[13] Admur 124/11; Yerushalmi Sukkah 5/1; Kaf Hachaim 139/40

[14] The reason: As the blessing was not instituted for the sake of the congregation but rather due to that it is proper for one who reads from the Torah to recite a blessing. Now, although it is an obligation upon the congregation to hear the blessing being said [as explained in 139/6] nevertheless the main part of the blessing is on his own behalf and not on behalf of the congregation, as is the case with Chazaras Hashatz. [Admur ibid]

[15] Admur 215/2

Other opinions: Some Poskim rule one is not obligated to answer Amen for a blessing that one did not hear at all and it is merely voluntary to do so. [Kaf Hachaim 124/47 and 139/40; Biur Halacha 215 “Chayav” based on Taz and Mamar Mordechai, brought in Piskeiy Teshuvos 215/3] Based on this some Poskim rule it is best not to answer Amen to such a blessing. [Kaf Hachaim ibid] If however one heard some of the words of the blessing then he must answer Amen. [Kaf Hachaim ibid; Michaber 215/2]

[16] Admur 46/1; M”A 46/8; Peri Chadash 46/3

The reason: The reason for this is because the obligation of Meiah Brachos is different than the obligation of other blessings, and thus is permitted to answer Amen even if one did not hear the blessing, even according to the first opinion in 124/11. [P”M 124 M”Z 4]

[17] Admur 46/1; M”A 46/8; Peri Chadash 46/3

Other opinions: Some Poskim rule that one fulfills his obligation of Meiah Brachos with answering Amen over the blessing even if he did not hear the blessing, so long as he knows which blessing it was. [Beis Yosef 46; P”M 124 M”Z 4]

[18] Rama 139/6; Beis Yosef in name of Orchos Chaim and Kol Bo; P”M 57 A”A 1; M”B 57/2 and Biur Halacha 57/2 “Veonim”; Kaf Hachaim 57/1; 139/42; Piskeiy Teshuvos 139/13

[19] Admur 124/11; 2^nd opinion in Admur 57/2 regarding Barchu and Admur concludes like this opinion; Rama 124/11; Orchos Chaim brought in Beis Yosef 124; Elya Raba 139/9; Elya Zuta 139/3; P”M 57 A”A 1; Siddur Beis Oved Barchu 1; Kitzur SHU”A 15/8; Ben Ish Chaiy Vayigash 17; Derech Hachaim; M”B 57/2; Kaf Hachaim 57/1; 139/42; Piskeiy Teshuvos 139/13

Other opinions in Admur regarding Barchu: Admur 57/2 states as follows: Some Poskim rule that if the Chazan said Barchu quietly then all the people who did not hear the Barchu from him may not answer to his Barchu. Rather, if they heard the congregation that is around the Chazan answering after the Chazan “Baruch Hashem” they are to answer Amen after them. [1^st opinion in Admur 57/2; M”A 57/1 [In contradiction to M”A 124/18, Vetzaruch Iyun Gadol-Kuntrus Achron 57/1]; Brachos 49b; Hagahos Hatur; Mamar Mordechai 57/1; Soles Belula 57/1; Shalmei Tzibur p. 89; Chayeh Adam 30/8; Chesed Lealafim 57/3; See Beis Yosef 139 “Kasav Rabbeinu Yechiel” who implies that whoever did not hear the Barchu may only answer Amen.] However, there is an opinion who says that if there are nine people who heard the Barchu from the Chazan and are answering Amen afterwards then the entire congregation may answer with them being that there are ten people saying a Davar Shebekidusha. [2^nd opinion in Admur; Rama 124/11 and 139/6 who writes “if the congregation did not hear”; Orchos Chaim brought in Beis Yosef 124; Elya Zuta 139/3] Practically, the main ruling follows the latter opinion, as ruled in 124/11 and in the M”A there. [Admur ibid] The reason for this is because so rules Rav Haiy Gaon, and so is proven from the Gemara in Sukkah 51b regarding the Alexandrian Shul, and this Gemara has no other explanation. Now, the M”A himself brings this Gemara in 124/18 and thus contradicts his ruling here, Vetzaruch Iyun Gadol. [ Kuntrus Achron 57/1]

The reason: Although some Poskim rule that any blessing that one is obligated in, he does not fulfill his obligation with answering Amen unless he hears the words of the blessing. Nevertheless, in this case, even they agree that he may answer without hearing the words. The reason for this is because he is not considered obligated in answering for the Barchu regarding this matter, as only those matters that one is obligated to recite even privately are included in the above stringency, and Kaddish/Kedusha/Barchu one is only obligated to say with a Minyan. [Admur 124/11; M”A 124/18]  This is proven from the shul of Alexandria who would answer Amen to Kadddish and Kedusha based on the waving of a flag. [M”A ibid; See Sukkah 51b]

[20] Biur Halacha 57/1 “Veonim”

[21] Piskeiy Teshuvos 139/13