Mincha:[1]

Ashreiy and Uva Letziyon:[2] Ashreiy and Uva Letziyon are not recited prior to Mincha, and are rather recited prior to Neilah.

Veani Sefilasi:[3] Veani Sefilasi is not recited even when Yom Kippur falls on Shabbos, being that its content is not relevant at this time.[4]

Kerias Hatorah:[5] During Mincha, a Torah scroll is removed, and the section of Arayos is read from Parshas Achareiy Mos.[6]

Haftorah:[7] Maftir Yona is read for Haftorah after the Mincha Torah reading.[8] The custom is to only say the first three blessings after the Haftorah, while the fourth blessing of “Al Hatorah Veal Haavoda is omitted.[9]

Tzidkascha:[10] The custom is to omit the prayer of Tzidkascha after Mincha.[11]

Birchas Kohanim:[12] The Kohanim do not recite the priestly blessing during Mincha, although the Chazan recites “Elokeinu Velokei Avoseinu”.

Beginning Neilah on time:[13] One is to begin Neilah at its proper time, as will be explained next. If needed, one is to skip Avinu Malkeinu [after Mincha] in order to begin Neilah on time.

In what Niggun is the Torah to be read in?[14]

The regular tune for Kerias Hatorah.

If one forgot to Daven Mincha, does he Daven Neilah twice?[15]

No. Rather he is to Daven Maariv twice.

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[1] Shulchan Aruch Chapter 622

[2] Siddur Admur; Custom of these provinces mentioned in 622/2

Ruling of Admur in Shulchan Aruch ibid: Some are accustomed to recite Ashreiy and Uva Letziyon prior to Mincha, as is usually done on every Mincha of Shabbos and Yom Tov. However, the custom of these provinces is to omit it from Mincha and rather recite it by Neilah, in order to separate between Mincha and Neilah. [622/2] Those who say it by Mincha are to also say it by Neilah for this reason. [623/1]

[3] Admur 622/3

[4] The reason: As it is said as a praise for the Jewish people that they returned to Shul on Shabbos after having eaten and drank. Hence, since eating is forbidden on Yom Kippur even when it falls on Shabbos, this praise is irrelevant. [ibid]

[5] Admur 623/4; Siddur Admur

[6] The reason: This portion is read in order so one who has transgressed such a sin should properly repent over it. The sin of Arayos is specifically chosen as it is commonly transgressed and peoples inclination are very strong in persuading them to do so. [ibid]

[7] Admur 623/4

[8] The reason: Being that it discusses the power of repentance and the fact that one cannot run away from Hashem. [Admur ibid]

[9] The reason: As the Avoda of the day was concluded prior to Mincha. [ibid]

[10] Admur 623/4; Siddur Admur

[11] The reason: The reason for this is because this prayer mentions judgment, and on Yom Kippur we pray for G-d to have mercy and go beyond the letter of the law. [ibid]

[12] Admur 623/6

[13] Admur 623/5

[14] Otzer Minhagei Chabad p. 233 brought in Hiskashrus 948 p. 13

[15] P”M 108 M”Z 5