The order of Davening on a fast day if Baal Bris [i.e. Mohel; Sandek; Father] is present:[1]

Tachanun [and Lamnatzeiach; Keil Erech Apayim]:[2]

If there is a Baal Bris present by the Minyan 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.

 Selichos:[3]

Even if there is a Baal Bris present by the Minyan, in which Tachanun is to be omitted, as stated above, nevertheless, Selichos is to be recited. [When saying it within the prayer, one is to begin from Keil Erech Apayim.[4] Some however are accustomed to say an abridged version of the Selichos.]

Does the Chasan or Baal Bris himself recite Selichos?[5] The Baal Bris does not recite Selichos.

Avinu Malkeinu:[6]

Even if there is a Baal Bris 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 Bris was to take place. However in other years the Rebbe recited it.]

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[1] See Pesakim Uteshuvos 264:43; See Encyclopedia Talmudit Vol. 4 Erech Bris Mila p. 248 footnotes 38-39

[2] Admur 602:4; Ketzos Hashulchan 24:7

[3] Michaber Michaber O.C. 131:5; Y.D. 265:13; Hashlama of Admur 131:7; Ketzos Hashulchan 24:7; Shevach Habris 13:3

[4] Kuntrus Hasiddur of Rav Avraham Chaim Naah 91; Shevach Habris 13:3

[5] Beis David 347; Avodas Hakodesh Kesher Gudal 19:24; Hashlama of Admur 131:7; Shaareiy Teshuvah 131:15; See Koreis Habris 264:69

[6] Admur 602:4; Rama 602:1 in name of Minhagim; Mateh Efraim 602:12