The blessing over Hallel:
Some Poskim rule that whenever half Hallel is recited, it is to be said without saying a blessing before or after. Other Poskim however rule that if the Hallel is being recited with a Minyan then a before and after blessing is to be recited, however an individual [praying without a Minyan] does not recite either blessing. Other Poskim however rule that every individual may recite a blessing even if he is not partaking in a Minyan. Practically the custom [of Sefaradim] in Eretz Yisrael and the surrounding cities is not to recite a blessing even in a Minyan. However the Ashkenazi custom is that every person recites a blessing even if he is Davening in private, without a Minyan. Nevertheless, one is to beware to try to recite Hallel with the Minyan. Furthermore, when reciting Hallel with the Minyan, only the Chazan is to recite the before and after blessing and he is to have in mind for the congregation to fulfill their obligation with him. In turn, the congregation is to answer Amen and fulfill their obligation with his blessing. [However if one is praying privately he is to recite the opening and concluding blessings of Hallel even when the entire Hallel is not recited and so is the Chabad custom. Furthermore many Chabad Chassidim are accustomed to recite the blessing on their own even when Davening with the Minyan. Some recite it prior to the Chazan and hence complete it prior to the Chazan completing his blessing. Others recite it together with the Chazan and some recite it after the Chazan.]
One is to recite a before and after blessing over Hallel on Rosh Chodesh. If one is saying Hallel with the Minyan one is to be Yotzei with his blessing, although many are accustomed to say the blessing to themselves even in such a case.
 422/2; See glosses of Siddur of Rav Raskin for an overview in this matter
 Second opinion in Michaber ibid; Rashi; Rambam Brachos 11/16; Chanukah 3/7
 The reason: As Hallel on Rosh Chodesh is a mere custom and we do not recite a blessing over fulfilling a custom. [Kaf Hachaim 422/34]
 First opinion in Michaber ibid; Rif Shabbos 24b; Rabbeinu Yonah Brachos 14a
 Definition of a Minyan: In general a Minyan refers to ten adult men. However see Admur 479/6 that if one is reciting Hallel without a Minyan it is a Mitzvah to have another two people listen and answer [for Hodu and Ana]. In explanation of the reason behind this some opinions say that a Zimun of three is considered a congregation which warrants a blessing to be said, and hence in order to say a blessing according to all one should least strive to have at least three people. [Lechem Chamudos brought in M”A 422/7; M”B 422/18; Kaf Hachaim 422/39]
 May every individual recite the blessing or only the Chazan? It is implied from the wording of the Michaber and Rama that according to this opinion every person may recite the blessing when Hallel is being recited with the Minyan and it is not necessary for the Chazan to be Yotzei the congregation. Thus, when saying Hallel with the congregation everyone can say the blessing. [See Admur 619/8 “and so is the law regarding Hallel” that ideally due to Berov Am Hadras Melech it would be proper to have only the Chazan recite the blessing, however the custom became for everyone to say it] However, in the Siddur Admur rules that only the Chazan is to say the blessing [as will be explained at the end of this Halacha]. The Shaar Hakolel 37/4 explains that this is in order to suspect for the stringent opinion which states a blessing is never recited, and hence by half Hallel Admur rules that only the Chazan should recite it. See Glosses of Rav Raskin on Siddur footnote 8 that suggests that perhaps even according to this opinion only the Chazan is to say the blessing and not every individual.
 Opinion of Rama ibid; Rabbeinu Tam Taanis; Tosafus Erechin 10b; Tur in name of Rosh
 The reason: Although everyone agrees that the saying of Hallel on Rosh Chodesh is a custom, nevertheless it is permitted to recite a blessing over a custom just like women are accustomed to recite a blessing over the Mitzvah of Lulav, even though they are not obligated in the Mitzvah. [Tosafus Erechin ibid; Kaf Hachaim 422/36]
 Michaber ibid
 Rama 422/2
The reason: This is initially required in order to recite the blessing even according to the first opinion [i.e. second opinion brought above]. [Biur Hagra; Kaf Hachaim 422/37]
 Siddur Admur; Mishnas Chassidim based on Kabala; Siddur Rav Amram
Ruling of Siddur ibid: “On days that Half Hallel is recited it should be accustomed that the Chazan alone says the blessing at beginning and end while the congregation listens to the blessings, answers Amen and fulfills their obligation.”
The reason and other opinions: It is implied from the wording of the Michaber and Rama that [according to the second opinion] every person may recite the blessing when Hallel is being recited with the Minyan and it is not necessary for the Chazan to be Yotzei the congregation. In Admur 619/8 he rules that ideally due to Berov Am Hadras Melech it would be proper to have only the Chazan recite the blessing by all Mitzvos, such a Shehechiyanu, Lulav and Hallel, however the custom became for everyone to say the blessing themselves being that in most cases the Chazan does not have in mind to fulfill their obligation. However, in the Siddur Admur rules that only the Chazan is to say the blessing. The Shaar Hakolel 37/4 explains that this is in order to suspect for the stringent opinion which states a blessing is never recited, and hence by half Hallel Admur rules that only the Chazan should recite it. See Glosses of Rav Raskin on Siddur footnote 8.
Reminding the Chazan: Many are accustomed to remind the Chazan before Hallel to have the congregation in mind within his blessing. [Shaar Hakolel 37/4]
 Siddur Admur; Regarding why Admur here directs the congregation to answer Amen: See Likkut Dinei Rosh Chodesh 7 footnote 9; Admur 215; 594/1; M”B 213/17
 Implication of Rama ibid; Tanya Rabasi 32; Hamanhig brought in Shaar Hakolel 37/5
 Sefer Haminhagim p. 69 [English]; Hayom Yom 1st Teves; Igros Kodesh 18/84 [printed in Shulchan Menachem 2/200]; Shaar Hakolel 37/5; Custom of Tzemach Tzedek [as brought in Shaar Hakolel ibid; however see Kuntrus Piskei Hasiddur]; Reshimos 8/20 that the Rebbe Rashab always said the blessing to himself even with a Minyan however he stated not to publicize this matter to others; See glosses of Siddur of Rav Raskin p. 475 for an overview in this matter
Ruling of Admur in Siddur and overview of Chabad custom: In the Siddur of Admur he does not write the law regarding an individual reciting Hallel and only writes regarding saying the blessing in a Minyan. The Shaar Hakolel 37/5 learns that Admur did not rule for us in this regard and hence one is to follow the ruling of the Rama that in our communities the custom is to recite the blessing. So was also heard to be the custom of the Tzemach Tzedek. Those Siddurim of Admur which state that a Yachid is not to say the blessing are inaccurate, as Admur never wrote these words and it was added by the publishers. Thus one is not to break from the accepted custom of the Rama. [Shaar Hakolel ibid] However see Glossses of the Rebbe Rashab on the Siddur who wrote that he asked his father the Rebbe Maharash about this issue and he replied that the Tzemach Tzedek told him that what was written in the Siddur by the publishers was most likely heard from the Maharil, and practically one can do as he chooses. Rav A”C Naah in Kuntrus Piskeiy Hasiddur also concludes that the Tzemach Tzedek never gave a final ruling on this matter, and he thus argues on the conclusion of the Shaar Hakolel ibid. Practically, the Chabad custom as stated in Hayom Yom is to say it.
 Reshimos 8/20 that the Rebbe Rashab always said the blessing to himself even with a Minyan however he stated not to publicize this matter to others; Sichas Kodesh 1981 4/322 [brought in Shaareiy Halacha Uminhag 2/175; Shulchan Menachem 2/194] “It is customary of Chassidim to quietly grab the blessing of Half Hallel”; See glosses of Siddur of Rav Raskin for an overview in this matter; See also Likkut Dinei Rosh Chodesh 8 footnote 8; Heichal Baal Shem Tov 29/42
 As is the simple implication of the Rebbe’s words and as is the simple understanding of Admur in 619/8 that when saying the blessing of Hallel to oneself one is to say it prior to the Chazan and answer Amen to his blessing. See glosses of Siddur of Rav Raskin ibid; So rules also Yesod Veshoresh Havodah 12/4 regarding reading Megillah, that the listeners may answer Amen to the Chazan’s blessing even if they already said their own blessing beforehand.
 As finishing the blessing prior to the Chazan causes an issue of an interval as how can one answer Amen prior to beginning Hallel after his blessing. So rules Yalkut Yosef Moadim 5/295 regarding the above case of Megillah; See Panim Meiros 2/5; Shaareiy Teshuvah 167/11; See glosses of Siddur of Rav Raskin ibid