The order of Davening on a fast day if a Chasan or Baal Bris [i.e. Mohel; Sandek; Father] is present:
Tachanun [and Lamnatzeiach; Keil Erech Apayim]:
If there is a Baal Bris or a Chasan [within seven days of his wedding, or on the day of his wedding] present by the Minya on a fast day then Tachanun, [Lamnatzeiach and Keil Erech Apayim] is omitted. [This omission includes the paragraph of Vehu Rachum recited on Mondays and Thursdays.]
Even if there is a Baal Bris or Chasan [within seven days of his wedding, or on the day of his wedding] present by the Minyan, in which Tachanun is to be omitted, as stated above, nevertheless, Selichos is to be recited. [Some however are accustomed to say an abridged version of the Selichos.]
Does the Chasan or Baal Bris himself recite Selichos? The Chasan himself or Baal Bris doed not recite Selichos.
Even if there is a Baal Bris or Chasan [within seven days of his wedding, or on the day of his wedding] present by the Minyan, in which Tachanun is to be omitted, as stated above, nevertheless, Avinu Malkeinu is to be recited. [Regarding the Chabad custom: There were years that the Rebbe omitted Avinu Malkeinu during Aseres Yimei Teshuvah if a Chasan was present, or a Bris was to take place. However in other years the Rebbe recited it.]
 Admur 602:4; Michaber 131:5 regarding Mila “If there is a Mila on a Taanis Tzibur then they say Selichos and Viduiy although do not do Nefilas Apayim or say Vehu Rachum”; Rama 602:1 in name of Minhagim; Elya Raba 133:13; Mateh Efraim 602:12; M”B 133:27 in name of Elya Raba and Magen Giborim “The same applies for a Chasan”; Ketzos Hashulchan 24:7
 Piskeiy Hassidur 151 and 179; Sichas Kodesh 6th Tishreiy 1975 based on Admur in Siddur that Lamnatzeiach is never recited when Tachanun is omitted. This ruling in the Siddur is based on Kneses Hagedola 131/3; Peri Chadash 131/1; Mamar Mordechai 131/6; Kaf Hachaim 581/78 states that so is the custom of Sefaradim.
Ruling of Admur in the SHU”A: In the Shulchan Aruch, Admur rules like Rama 131/1 that Lamnatzeiach may be recited even on a day that Tachanun is omitted. [Admur 429/12; 602/4 [in parentheses]]
 Siddur Tehilas Hashem [from 1978 and onwards with the Rebbe’s approval] based on Sichas Kodesh 6th Tishreiy 1975 that the Rebbe equates Kel Erech Apayim with Lamnatzeiach. See Shulchan Menachem 3/293; Glosses of Rav Raskin p. 165; Hiskashrus 438 p. 17; To note however that the Rebbe himself did recite Kel Erech Apayim even when Tachanun was not recited. [Rav Raskin ibid]
Ruling of Admur: In the Shulchan Aruch [429/12; 602/4] Admur rules that Kel Erech Apayim is recited with exception for Erev Pesach. This follows the ruling of the Hagahos Maimanis; Darkei Moshe 602 brought in Kaf Hachaim 602/12. [Some explain that it is for this reason that Admur in 602/4 placed this ruling in parentheses, as it is not brought in previous Poskim in Shulchan Aruch. [Shulchan Menachem ibid footnote 2] Vetzaruch Iyun as it is brought by Admur in 429/12 without parentheses, and is likewise clearly implied from the Rama 429/2] To note that also in the Siddur before Kel Erech Apayim Admur lists a number of days that it is to be omitted on, thus implying it is not always omitted when Tachanun is not said.
Ruling and explanation of Divrei Nechemia: The Divrei Nichemia 131 brings three opinions regarding the saying of Keil Erech Apayim: 1) It is only omitted by a day that Hallel is recited or a day that ahs the status of a Yom Tov like Erev Pesach. [This is the opinion of the Rama 429/2] 2) It is omitted on every Erev Yom Tov and on Isru Chag. 3) Every day that Tachanun is omitted so is Lamnatzeiach. [so rules Peri Chadash 131] The Divrei Nechemia concludes that by Lamnatzeiach we rule like the third opinion, however by Keil Erech Apayim we rule like the opinion that rules it is to be recited.
The reason behind the Rebbe’s ruling: The Rebbe explains that the ruling in the Shulchan Aruch of Admur follows the ruling of the Rama that differentiates between the laws of Tachanun and that of Lamnatzeiach. However according to Admur in the Siddur that rules Lamnatzeiach is always omitted when Tachanun is not said then likewise Kel Erech Apayim is to be omitted in all days that Tachanun is not said. [Sichas Kodesh ibid, printed in Shulchan Menachem ibid] As for the reason why Kel Erech Apayim is omitted this is because it mentions sin, and we do not desire to mention sin on any day that Tachanun is omitted. [See Shaar Hakolel 36/2; Shulchan Menachem ibid footnote 5]
 Michaber ibid
 Michaber 131:5 regarding Mila; Elya Raba 133:13; M”B 133:27 in name of Elya Raba and Magen Giborim “The same applies for a Chasan”; Ketzos Hashulchan 24:7
Regarding Selichos of Elul: See Pnei Meivin Yoreh Deah 319; Ketzei Hamateh 602:22; Pischeiy Teshuvah 581; Glosses of Shoel Umeishiv on 602; Alef Hamagen 581:38 in gloss; Sheivet Halevi 4:54; Levushei Mordechai 226; Mechzeh Avraham 154; Betzeil Hachochma 4:146; Piskeiy Teshuvos 581:4
 The reason: As it suffices to omit part of the prayer in honor of the Chasan and it is not necessary to omit it completely. [Taz 133:13; M”B 133:28]
Regarding saying Ashamnu: The Michaber ibid rules that Viduiy is recited within Selichos. The Kaf Hachaim 133:92 writes that it is to be said before Davening. The Piskeiy Teshuvos 131 footnote 151 writes that the Viduiy is recited [however in 581:4 he writes Viduiy is not recited]. However, the Ketzos Hashulchan ibid writes that one skips all Tachanun and Nefilas Apayim, hence implying that Viduiy is not recited and so is the Chabad custom. [see Shulchan Menachem 3:83] Vetzaruch Iyun
 Luach Eretz Yisrael; Tzitz Eliezer 7:9; Piskeiy Teshuvos 566:5
 Shaareiy Teshuvah 131:6; P”M 131 M”Z 12; Divrei Nechemia [Hashlama] 131:7; Ketzos Hashulchan ibid footnote 28 in name of Divrei Nechemia
Regarding Selichos of Elul: The Chasan or Baal Bris recites Selichos as usual, without Tachanun. [Nitei Gavriel 16:8; Directive of Rebbe to Rabbi Leibel Groner when he was a Chasan during Selichos. Shulchan Menachem 3:83]
 Admur 602:4; Rama 602:1 in name of Minhagim; Mateh Efraim 602:12
 6th Tishreiy 1935 the Rebbe did not say Avinu Malkeinu because there was a Chasan in the Minyan and the Rebbe than explained it in a Sicha on that day that according to Admur in the Siddur Avinu Malkeinu is never recited when Tachanun is omitted. [See Shulchan Menachem 3/293; Otzer Minhagei Chabad p. 166; Glosses of Rav Raskin p. 165;]
 Shulchan Menachem ibid footnote 7 that there were many instances after this Sicha was recited that the Rebbe said to recite Avinu Malkeinu even when a Chasan or Baal Bris was present. See also Sichos Kodesh 1980 p. 865 “On Monday Tzom Gedalia after Selichos the Chazan began saying Kaddish. The Rebbe motioned to him and told him to say Avinu Malkeinu. The Rebbe was then told that there is a Chasan.” [It does not state what they did in the end. However, it seems clear that the congregation in 770 accepted this earlier ruling of the Rebbe that Avinu Malkeinu is not recited. However, the Rebbe himself seems to have retracted from this ruling, as he knew that a Chasan was already there, as why else did the congregation omit Tachanun prior to Selichos. Hence it seems the Rebbe, which certainly knew there was a valid reason not to say Tachanun, ruled that nevertheless Avinu Malkeinu is to be recited.] See Hiskashrus 438 p. 17 footnote 9