After concluding all the Tekios that are blown after Musaf one may not blow the Shofar any longer if there is no reason to do so.
Children: It is permitted for one to tell children to blow the Shofar on Rosh Hashanah for the sake of practice. This applies to all children whether they are above or below the age of Chinuch. It is permitted for children to blow throughout the entire day even after they heard Shofar in Shul [and hence already fulfilled the Mitzvah].
May a man blow Shofar for women? It is permitted for a man to blow Shofar for women even if he has already fulfilled his obligation.
On Rosh Hashanah one is only allowed to blow the Shofar in order to fulfill the Mitzvah or for practice for that day. It is forbidden to blow it casually or for practice for the next day. It is however permitted for children to practice blowing the Shofar on Rosh Hashanah even for no need at all.
If one is unsure if he fulfilled his obligation, or desires to fulfill his obligation according to all opinions, may he blow the Shofar after the Davening in Shul?
If one is Davening without a Minyan may he to blow 100 sounds as is the normal custom when Davening with a Minyan?
Does the Shofar become Muktzah after one completes the Mitzvah of blowing?
No. The Shofar is fit to be used throughout the day, such as for children to practice, or for blowing for someone who did not yet hear the sounds and hence it is not Muktzah.
May one blow the Shofar on behalf of children above the age of Chinuch if he already fulfilled his obligation?
Yes. Nevertheless the child is to say the blessing and not the Baal Tokeia.
May one blow the Shofar on behalf of children below the age of Chinuch?
It is implied from the Poskim that it is forbidden to do so unless the child is learning how to blow in the process. Practically this matter requires further analysis.
On Mivtzaim may one blow Shofar on behalf of a small child on the behest of the child’s mother or father? Based on the above one must beware from blowing Shofar for a child below the age of Chinuch if there is no one else also fulfilling their obligation. One may however have another child blow the Shofar on their behalf.
May one teach a child on R”H how to blow the correct sounds?
May one practice blowing Shofar for the sake of blowing that day?
 596/2; Rama 596/1; Darkei Moshe 588; Maggid Mishneh Shofar 2/7; Yireim; M”A 596/2; Elya Raba 596/1[be stringent]; Chacham Tzvi 35; M”B 596/3 [that so rules majority of Achronim, which are the M”A; Karban Nesanel; Bigdei Yesha; Yeshuos Yaakov; Chemed Moshe; Nehar Shalom; Mamar Mordechai-Shaareiy Tziyon 596/4]; M”E 506/1; Chayeh Adam 142/19
Other Opinions: Some Poskim rule that it is completely permitted to blow Shofar on R”H without limitation and there is never a prohibition involved. [Or Zarua brought in Darkei Moshe ibid; Taz 596/2; Birkeiy Yosef 596/1; Panim Meiros 102] The Darkei Moshe ibid negates his opinion and so he concludes in Rama ibid. The Taz ibid questions the ruling of the Rama and rules that there is never a prohibition to blow Shofar on Yom Tov. The Chacham Tzevi ibid argues on the Taz ibid and brings proofs to defend the ruling of the Rama. The Panim Meiros ibid answers the questions of the Chacham Tzevi and explains that even the Taz only allowed it to be blown on R”H and not by another Yom Tov. The Elya Raba ibid brings both opinions and concludes that one is to be stringent. The Birkeiy Yosef ibid concludes that he has not seen people be careful in this. See Beir Heiytiv 596/1; Shaareiy Teshuvah 596/1; Kaf Hachaim 596/4
 The reason: As blowing the Shofar [not for the Mitzvah] is Rabbinically forbidden on Yom Tov. It was only permitted to be done on R”H [even not for the Mitzvah] if doing so has a need such as to satisfy the women to blow for them. Likewise those that are accustomed to blow the Shofar after Davening, since they do so for the reasons known to them, therefore the Sages permitted it. The reason the Sages were lenient in a time of need to allow blowing the Shofar is because the blowing of the Shofar is not a complete Shvus [Rabbinical Melacha] but merely a mundane act. However to blow it for no need at all is [forbidden being that it] is a belittling of Yom Tov. [Admur ibid]
 Admur ibid; M”A 596/2; Elya Raba 596/1; Chayeh Adam 142/19; M”E 596/1; M”B 596/4; Kaf Hachaim 596/5
 The reason: The reason is because we are knowledgeable in the date of the month and know that the 1st day is the real day of R”H while the 2nd day is ideally a weekday. Thus one who blows on the first day on behalf of the 2nd day is in truth blowing sounds that are not needed for the sake of Yom Tov and is blowing them for the sake of a weekday. [Admur ibid]
 Admur ibid; Rama ibid; M”E 596/3
 This allowance applies whether to the father or any other adult. [P”M 596 A”A 3; M”B 596/5; Kaf Hachaim 596/9]
 However it is forbidden to blow Shofar on their behalf once they have already fulfilled their Mitzvah, unless one is doing so in order to teach them how to blow. See Q&A!
 The reason: As it is a Mitzvah upon the adults to teach the children [how to blow] and educate them in Mitzvos. [Admur ibid] Thus since the adult himself is fulfilling the Mitzvah of Chinuch by telling the child to blow, therefore it is permitted to be done. [M”A 596/3]
 589/2; See Halacha 1B!
Other Poskim: Some Poskim rule it is forbidden for men to blow the Shofar on behalf of only women as it is forbidden to blow the Shofar for no need. [Baal Hitur brought in Tur 589; Peri Chadash; See M”E 589/12]
 Piskeiy Teshuvos 596/2; Mishmeres Shalom 41/6 [that they blew the Shofar after Davening as the opinion of Rashi in the Shiur of the Shever]
 Piskeiy Teshuvos 592/3
 Rashal 40; Kneses Hagedola; Taz 596/2; Elya Ra 596/1; M”E 596/2; M”B 596/3; Kaf Hachaim 596/7
 Peri Megadim 589 A”A 4; Chayeh Adam 140/7
 If the child knows how to say the blessing then this follows the same ruling as any time one is blowing for another in which case the person fulfilling the Mitzvah is to say the blessing . [See Halacha 9F]
If the child does not know how to say the blessing: The P”M ibid writes that the adult may say the blessing on behalf of the child since he is obligated in Mitzvos, however he concludes with a Tzaruch Iyun. The Piskeiy Teshuvos 589/2 writes based on this that the adult is not to say the blessing.
 Az Nidbaru 13/38
 Chanoch Lanaar 22/7 based on the Poskim that rule one may not blow for women if he already fulfilled his obligation. Hence by a child one is to be stringent.
 As perhaps it is only permitted to tell the child to blow and not to blow the Shofar for the child [as is inferred from the wording of Admur ibid “It is permitted to tell the child”]. The reason is because there is a Mitzvah of Chinuch involved in teaching the child how to physically blow the Shofar, even if he is below Chinuch. However to blow for a child below Chinuch there is no purpose at all as what does he learn from it. The difference between a child below Chinuch and a woman is that a woman intends to do the Mitzvah [as all Mitzvas that are Zman Grama in which they receive reward] however a child below Chinuch does not perform a Mitzvah at all. This is also clearly implied from the source of the ruling of Admur ibid which is [the Rama ibid who took it from] the Maggid Mishnah [Rambam Shofar 2/7]. The Maggid Mishneh writes that Rashi states “One may practice with them, not that the Gadol may blow etc from here we learn that a Gadol cannot blow Shofar for no reason once he fulfilled his Mitzvah.” Thus the entire source for forbidding blowing for no reason is from this allowance to educate children how to blow, and on this the Maggid Mishneh says explicitly “however not the Gadol”. [Vetzrauch Iyun on the source of the Maggid Mishneh in Rashi as I have not found it in any Rashi, neither in R”H 32b; Erechin 2b or Eiruvin 96b; and so writes the Lechem Yehuda Hilchos Shofar that he has not found the source of these words of Rashi] Vetzaruch Iyun!
 M”B 596/5; Kaf Hachaim 596/10
 Leket Yosher [student of Terumos Hadeshen] p. 125 [“One who is not an expert in blowing may practice on R”H in the morning”]; Piskeiy Teshuvos 596 footnote 7