[It is customary to blow the Shofar after the conclusion of the prayer of Musaf. Various custom exist regarding how many sounds one is to blow.] Some communities have the custom after the prayer to blow a long Teruah [“Teruah Gedola”] without a Tekiah. Other communities have the custom to repeat thirty blows [after Musaf]. Other communities have the custom to blow [a total of] 100 blows [throughout the day]. They hence blow after Davening whatever amount of blows needed [to reach the total of 100] after calculating the amount of blows that were sounded in Meyushav [after Kerias Hatorah] and Meumad [Musaf]. [Practically the widespread custom is like this latter opinion, to blow the remaining sounds for a total of 100 blows and by the last blow they sound a Tekiah Gedola [and not a Teruah Gedola]. The Chabad custom is to follow all three customs mentioned above. We blow ten blows [Tashrat Tashat Tarat] after Musaf [to complete the total of 100 blows, as rules the 3rd custom]. We do not sound a Tekiah Gedola by the last Tekiah of the ten sounds. We then blow another thirty at the conclusion of Davening, after Tehillim [as rules the second custom]. The last Tekiah sounded at the end of these thirty blows is a Tekiah Gedola [as rules the first custom regarding a Teruah Gedola].]
The Chabad custom is to blow ten blows after Musaf and another thirty at the conclusion of Davening, after Tehillim. The last Tekiah of the thirty is sounded as a Tekiah Gedola.
Must one repeat the sound if he made a mistake in the blows of after Musaf?
No, unless one knows that there is someone present who did not yet fulfill his obligation
If the congregation forgot to blow the sounds after Musaf must they do so at a later time?
No, they are not required to do so.
In how many breaths is the Shevarim-Teruah of the blows of after Musaf to be sounded in?
The Shevarim-Teruah contained within the sounds that are blown after Musaf [i.e. ten in middle of Kaddish and thirty after Tehillim] are to be blown in one breath.
If one is Davening without a Minyan is he to blow the above sounds after Musaf?
The custom is to blow whatever sounds remain to accumulate 100 blows.
 Michaber 596/1; first custom brought in Admur ibid; Tur in name of Rav Amram
 The reason: This is done in order to confuse the Satan [Divine prosecutor] from prosecuting that we are not scared of G-d’s judgment. As being that after prayers we proceed to have a festive meal with food drink and merrymaking the prosecution may use this to find fault with us that we are not afraid of the day of judgment. [Thus the final Shofar blowing prevents this prosecution]. [Admur ibid; Taz 596/1] Alternatively the reason is in order to push away the Kelipos from nurturing from the Holiness that was drawn down through the prayer of the day. [Kaf Hachaim 596/1]
 Rama 596/1; Darkei Moshe 596; second custom brought in Admur ibid
 The reason: As they suspect that perhaps some people in the congregation did not properly hear all the blows and hence they will now fulfill their obligation with hearing these blows. [Admur ibid] However the Levush 596 writes that the reason is in order to confuse the Satan. This is similar to the first reason mentioned above. In the Machzor Chabad it states the reason of the Levush that the 30 blows are sounded to confuse the Satan and does not mention the reason of Admur.
 Third custom brought in Admur ibid; M”A 596/1 in name of Shlah based on Arizal in Shaar Hakavanos p. 99; Peri Eitz Chaim 26/3; Hearuch “Meiah Piyos” [that so is their custom]; Hamanhig R”H 21; Tosafus R”H 33b in name of Aruch
 M”B 596/1; M”E 596/1; Kaf Hachaim 596/2; 592/5
How many blows are sounded? There are various customs in regards to how many blows are sounded after the prayer. This depends on how many blows were sounded during prayer. [See Machatzis Hashekel 596/1; Kaf Hachaim 5963] Those communities that don’t blow the Shofar during the silent prayer of Musaf blow 30 blows after Musaf and another 10 blows at the end of Davening, prior to Anim Zemiros. [M”B 592/4; M”E 592/11; Luach Eretz Yisrael] Those communities that blow 30 blows also during the silent Musaf prayer only blow 10 blows after Musaf. These blows are sounded in middle of Kaddish prior to Tiskabel. [Shlah in name of Arizal; Siddur Admur]
A Tekiah Gedola after Tekios Meyushav: It is customary to sound an extra long Tekiah by the concluding blow of the Tekios Meyushav. [Siddur Torah Or and Machzor [omitted in Siddur Slavita of Admur]; Siddur Arizal; Siddur Shlah; Minhagei Mahril R”H; Minchas Elazar 2/65; Darkei Chaim Veshalom 720; Siddur Yaavetz; Siddur Daas Kedoshim; Piskeiy Teshuvos 596/1] The reason this is done is in order so the congregation knows that the blows have ended and they should begin saying Ashrei Haam. [Mahril ibid]
 As we blow 30 by Meyushav; 30 by the silent prayer of Musaf and 30 by the repetition of Musaf for a total of 90. Ten more blows are sounded for a total of 100.
 Siddur Admur
 Siddur Admur; Otzer Minhagei Chabad 334-335
 Sefer Haminhagim p. 120; based on the second custom mentioned above in Admur ibid; This follows the order written in Shlah p. 217 that even after completing the 100 blows as rules the Arizal one is to blow 30 blows after Aleinu. However see Kaf Hachaim 592/5
 In all the new printings of the Machzor Chabad they specifically write that the last Tekiah of the 30 after Tehillim is to be a Tekiah Gedola. [see printing of Machzor Kehos 2006 in both the English and the Hebrew version] However in all previous prints of the Machzor this was omitted and it simply writes “Tashat” as the ending set, without mentioning that it should be a Tekiah Gedola. In Otzer Minhagei Chabad 337 and 335 he evidently understood from this that we do not blow a Tekiah Gedola at the conclusion of the thirty blows after Tehillim.
 Admur 590/18; Bach 596
 Levush 596 brought in Machzor Chabad; Tur 596 in name of Rav Haiy Gaon; Bach 596
 Shevach Hamoadim p. 30; Otzer Minhagei Chabad 339; Hiskashrus footnote 78; Heard from Rav Tenebaum, the Baal Tokeia in 770 in those years that the Rebbe did not blow, that so was the custom in Otvotz by the Rebbe Rayatz and so is the custom in the Rebbe’s Shul in 770. [Shevach Hamoadim ibid] However see Otzer 281-282 that the Rabbeim blew even the Shevarim Teruah of Meyushav in two breaths. Vetzaruch Iyun!
 Piskeiy Teshuvos 592/3