The evening prayer when Yom Kippur falls on Shabbos:
Kabalas Shabbos and Maariv: When Yom Kippur coincides with Shabbos, one begins the Maariv prayer from Mizmor Ledavid [psalm 29], [omitting all the Psalms from Lechu Neranina until Mizmor Ledavid]. [One recites the entire dialect from Mizmor Ledavid and onwards, including Ana Bekoach; all the stanzas of Lecha Dodi; Mizmor Shir, Kegavna. In Lecha Dodi, the normal dialect of Berina is recited. After Shemoneh Esrei one recites Vayechulu, and Meiyn Sheva. Following the recital of Meiyn Sheva one recites Selichos, Viduiy, Ledavid Mizmor and then Kaddish with Tiskabel. This Kaddish is then followed by “Mizmor Ledavid Hashem Roiy” as is usually recited on Friday night. One then recites half Kaddish, Barchu and Aleinu.]
Vayechulu and Meiyn Sheva: When Yom Kippur falls on Shabbos, the Chazan recites Mieiyn Sheva after Shemoneh Esrei of Maariv, as is always done on Friday night. Hamelech Hakadosh is to be recited in place of Hakeil Hakadosh. [Likewise, when the congregation customarily recites the paragraph of Magen Avos they say the words Hamelech Hakadosh in place of Hakeil Hakadosh.] The Chazan, however, concludes only with the blessing of Shabbos [i.e. Mikadeish Hashabbos] even if Yom Kippur falls on Shabbos.
If in Meiyn Sheva the Chazan said Hakeil Hakadosh instead of Hamelech Hakadosh must he repeat the Meiyn Sheva?
This matter is disputed amongst Poskim. Some Poskim rule if he completed the blessing, then the blessing must be repeated from the beginning. Others rule it is not to be repeated. Practically the Chazan is not to repeat the blessing. Nevertheless if the Chazan remembers prior to saying G-d’s name in the blessing of Mikadeish Hashabbos then he is to go back and say it.
 Siddur Admur regarding Yom Tov; Ketzos Hashulchan 77/2; Shaar Hakolel 17/6 states that this was mistakenly omitted from certain prints of the Siddur
Ruling of Admur in Shulchan Aruch: In the Shulchan Aruch 619/10, Admur rules that Kabalas Shabbos is not recited, although Mizmor Shir Leyom Hashabbos is recited before Barchu. So also brings M”E 625/41In the Siddur, however, Admur rules to begin from Mizmor Ledavid and so is the Chabad custom.
 The reason: Some write the reason is because there is a Mitzvah of Simcha on Yom Tov and we hence desire to speed the conclusion of Maariv. [Otzer Minhagei Yeshurun p. 64; See Admur 270/1 regarding Bameh Madlikin that it is omitted on Yom Tov in order to hasten Simchas Yom Tov] Alternatively, the reason is because these Psalms contain the words Rina, and on Yom Tov we emphasize the words Simcha. [Ketzos Hashulchan 77 footnote 13] Alternatively the reason is because the first five Mizmorim until Mizmor Ledavid relate to the five weekdays until Erev Shabbos while the psalm of Mizmor Ledavid relates to Erev Shabbos. Hence, we omit the first five Zemiros as it is not proper to relate them to Yom Tov. [Sichas Kodesh 2 p. 121] To note that the Mitzvah of Simcha does not apply on Rosh Hashanah, and hence we recite Berina in Lecha Dodi as a normal Shabbos, thus the only reason that explains why on Rosh Hashanah we omit these Psalms is the last reason mentioned. [Glosses of Rav Raskin on Siddur p. 250]
 Shaar Hakolel 17/6; Ketzos Hashulchan 77 footnote 13; Otzer Minhagei Chabad p. 63
Other customs: Some are accustomed to only recite the first and last stanza of Lecha Dodi. [M”E 625/41] Others recite the first two stanzas of Lecha Dodi corresponding to Zachar and Shamor. [Alef Hamagen 625/56] Others recite the entire Lecha Dodi with exception to the stanza of Hisnaari Meiafar Kumi which is omitted. [Peri Megadim] Some are accustomed to omit Kegavna being that it mentions that all the other days are filled with wrath which is untrue regarding Yom Tov. [Siddur Yaavetz; Likkutei Mahrich Pesach; Alef Lamateh 625/67; Divrei Torah 9/72; Piskeiy Teshuvos 487/3]
 Sefer Haminhagim p. 52 [English]; Rebbe in Machzor Chabad; Luach Kolel Chabad [Edited]; Implication of instructions in Siddur Yaavetz; M”E 582/2; See Otzer Minhagei Chabad p. 62; Glosses of Rav Raskin on the Siddur
The reason: The Rebbe [in a footnote on the Machzor ibid] explains that Rosh Hashanah and Yom Kippur are not given for days of rejoicing [see Admur 582/10] and hence we do not change from the normal wording of Berina.
Other Yomim Tovim: By other Yomim Tovim the custom is to interchange the word Berina for Besimcha. [Hagahos Hasiddur of Rebbe Rashab; Ketzos Hashulchan 77/2; Mishnes Chassidim “Leil Yom Tov” 1/2].
Difference between Rina and Simcha: The term Rina denotes a bittersweet joy, a joy that comes as a result of a previous distance. However Simcha does not have any bitterness mixed with it at all. [Magen Avos Vayishlach’ Ketzos Hashulchan 77 footnote 13] Accordingly it is understood why on Rosh Hashanah we do not recite Besimcha, as there is bitterness involved in the repentance required.
Other customs: Some are accustomed to recite Besimcha even on Rosh Hashanah. [Minhag Rav Ahron of Belz, brought in Piskeiy Teshuvos 582 footnote 20]
 Mateh Efraim 582/2; Otzer Minhagei Chabad p. 63
 The above order is written in Piskeiy Hasiddur footnote 40; Otzer Minhagei Chabad p. 69
 Admur 619/10 and 582/4
 The reason: The reason why we do not mention Yom Tov [Rosh Hashanah or Yom Kippur] within this blessing of Meiyn Sheva is because its entire reason of being said only relates to Shabbos, as on a regular Yom Tov Meiyn Sheva is not recited. It is recited on Shabbos not due to the holiness of the day [which would thus warrant it to be recited also on Yom Tov] but rather due to Mazikin [damaging forces]. It is thus not similar to the law that requires Shabbos to be mentioned in Nielah of Yom Kippur, that although Neilah is never recited on Shabbos and is only recited due to Yom Kippur, nevertheless one is required to mention Shabbos in the Shemoneh Esrei. This is because Yom Kippur obligates four prayers to be recited, which is Shacharis, Musaf, Mincha, and Neilah, and thus one must mention Shabbos in each prayer. However here the blessing of Meiyn Sheva was not instituted due to the holiness of the day [as was Neilah of Yom Kippur] but simply due to the Mazikin. [269/14]
 584/5; 602/2; Rama 584/1; 602/1; Rivash 512; Kneses Hagedola 584/2; Peri Chadash; Kisei Eliyahu 584/3
Other opinions: Many Poskim rule that Avinu Malkeinu is to be recited even on Shabbos. [Rashbatz 3/186 brought in Beis Yosef; Hatanya; Mateh Yehuda 584; implication of Arizal in Shaar Hakavanos; see Kaf Hachaim 584/8] Based on the Arizal ibid it appears that one is to recite all the stanzas of Avinu Malkeinu, with exception to the one’s that mention sin, even on Shabbos Shuva, and so is the custom of the Beis Keil community in Jerusalem. [Kaf Hachaim 582/16] The Kaf Hachaim 584/8 concludes: It seems that the Ashkenazi custom is to omit it while the Sefardic custom is to say it and for this reason the Michaber omitted this ruling from his Shulchan Aruch. Each community is to follow their custom.
 The reason: As it is forbidden to request one’s needs on Shabbos. [ibid; Ran] Alternatively, the reason we omit it on Shabbos is because the entire reason that we recite Avinu Malkeinu is in correspondence to the middle blessings of Shemoneh Esrei that are omitted on Yom Kippur during the week. [Levush brought in Kaf Hachaim 584/7]
Does this also apply to private requests? Some suggest that only a set prayer of request was negated on Shabbos Yom Kippur while a private request is not only allowed but is motivated to be expressed. [Piskeiy Teshuvos 582 footnote 21]
 Admur 623/9
The reason: As now is the final signing of the decree and we require supplication for mercy and if not now then when. [admur ibid]
 See Kaf Hachaim 582/18; Mateh Efraim 582/5; Alef Lamateh 582/1; Alef Hamagen 582/17; Piskeiy Teshuvos 582/6
 M”B 582/10
 Kneses Hagedola 582/5; Elya Raba 582/2; Mateh Yehuda; Mateh Efraim 582/5; Shalmei Chagiga in name of Mahariy Iash [brought in Alef Lamateh ibid]; Machazik Bracha 582/3; Shalmei Tzibur 197; Zechor Leavraham 3/143; Shaareiy Teshuvah 582/3; Ben Ish Chaiy Netzavim 18
The reason: The Chida in Machazik Bracha explains that according to Kabala there is a mystical reason behind reciting Meiyn Sheva and hence it must be repeated if not recited properly. [Kaf Hachaim ibid]
 If however he did not yet complete the blessing then he returns to the words Hamelech Hakadosh and reads from there and onwards. [ibid]
 Peri Chadash [brought in Kaf Hachaim ibid]; Gan Melech 149; Siddur Derech Hachaim; Peri Megadim 582 A”A 2 ; Nishmas Adam; Yeshuos Yaakov; Pischeiy Teshuvah in name of Divrei David 55; Alef Hamagen 582/17; Kitzur SHU”A 129/4
The reason: As the entire blessing of Meiyn Sheva is only recited use to Sakana, and hence we do not require its repetition if a mistake was made. [Peri Chadash ibid]
 Likkutei Mahrich; Luach Eretz Yisrael; Piskeiy Teshuvos 582/6; The Kaf Hachaim ibid concludes that one who does not repeat the blessing is not to be protested, although it seems he leans like the stringent opinion viewed by the Chida, based on Kabala. See Yabia Omer 2/29.
 M”B ibid; M”E ibid; See Peri Chadash ibid that “although if he is still within Kdei Dibbur we protest him and make him return”. Vetzaruch Iyun as to which part of the prayer he is referring to Kdei Dibbur of? The words Hakeil Hakadosh or the concluding blessing.