Gemara

(Mishnah): We do not take securities [for Machatzis ha'Shekel] from Ketanim.

Inference: We do not take a security from Ketanim, but we do demand the Shekel.

This is only if he brought two hairs [of puberty].

We do not take a security even if he brought two hairs.

Chulin 24b (Beraisa): When a man's beard is full, he is proper to be appointed Shali'ach Tzibur and descend [to pray] in front of the Teivah (podium);

Megilah 24a (Mishnah): A child may not be Pores Al Shma (say Borchu and the first Berachah before Shma) or descend in front of the Teivah.

Rishonim

Rambam (Hilchos Tefilah 8:1): We appoint to be Shali'ach Tzibur only one who is great in Chachmah and deeds. If he is old, this is very praiseworthy. We strive that his voice should be pleasant and he regularly reads [written Torah]. If one's beard did not fill out, even if he is a big Chacham he may not be Shali'ach Tzibur, due to Kevod Tzibur. He may be Pores Al Shma from when he brings two hairs after 13 years.

Rosh (Megilah 3:15): Here we say that a child may not descend in front of the Teivah. In Chulin, we require a full beard. That is to appoint him to be a fixed Shali'ach Tzibur. Here we discuss on a haphazard basis.

Ran (Chulin 5b DH Garsinan): Rashi explains that our Gemara discusses being appointed Shali'ach Tzibur for all needs - to blow the Shofar, excommunicate, be appointed a leader and to descend in front of the Teivah and pray (for the Tzibur). I disagree. Being appointed a leader and other needs are not called Shali'ach Tzibur, rather, Chazan ha'Keneses! Rather, it discusses only to descend in front of the Tevah and pray. The Gemara said "Shali'ach Tzibur", and not just "to descend in front of the Tevah", for we require a full beard only to appoint him to be a fixed Shali'ach Tzibur. On occasion, when there is no one else, as long as he is an adult he may descend. Megilah 24a says that a child may not descend in front of the Teivah. This connotes that any adult may do so occasionally. R. Natrunai Ga'on answered like this.

Rishonim

Bartenura (Shekalim 1:3 DH u'Ketanim): Even if he brought two hairs, and he is less than 20 years [we do not take a security from him].

Tosfos Yom Tov (1:4 DH Kol (2)): The Bartenura obligates only above 20. The Mishnah says "Ketanim". Presumably, this is until 13 years, like it normally means. The Rambam says so in Perush ha'Mishnayos and the Mishneh Torah, and the Ramban on Chumash says so. The Yerushalmi explicitly says so.

Tosfos (Berachos 26a DH Iba'i): The seven Berachos of Musaf were enacted only due to "u'Nshalmah Parim Sefaseinu" (our words should be accepted in place of the Korbanos). Therefore, if it was not said in time, there is no compensation.

Tzitz Eliezer (11:1): Based on this, may one below 20 be the Shali'ach Tzibur for Musaf, according to those who exempt him from giving Shekalim? R. Akiva Eiger (Teshuvah 9) said that one exempt from Shekalim, e.g. a woman, has no obligation of u'Nshalmah Parim Sefaseinu, so she is exempt from Musaf. Sha'arei De'ah (1:17) wrote "l'Chatchilah one should be careful that the Shali'ach Tzibur be at least 20. The Yerushalmi says that we do not take a security below 20. Perhaps they cannot be Motzi others above 20." Really, the Rambam and Ramban disagree, and the Tosfos Yom Tov says that the Yerushalmi supports them. In any case l'Chatchilah it is good to fulfill all opinions. The Torah Temimah (Shemos 30:13(22)) said "the Chinuch, Roke'ach and Gra on the Yerushalmi exempt below 20, like the Bartenura. If so they are exempt from Musaf and should not be Shali'ach Tzibur. This is a great Chidush; this requires great investigation." Also China d'Chayei says so.

Tzitz Eliezer: Even people meticulous about Mitzvos are not careful about this. The Rema (694:1) exempts those below 20 from Zecher l'Machatzis ha'Shekel, like those who exempt. We are normally stringent for his opinion! It seems that all obligate from 13 until 20, just we do not take a security, therefore he can be Motzi others. Taklin Chadtin and Korban ha'Edah say that he is liable only mid'Rabanan. There is no hint in the Yerushalmi for this. Rather, Chachamim enacted not to take a security below 20, for he is not so established financially.

Mesores Moshe (OC 140): Ha'Gaon R. Moshe. Feinstein Ztz"l said that even if only men above 20 gave, also women and youths had a share in Korbanos Tzibur. It is unreasonable to exempt men below 20 from Musaf.

Poskim

Shulchan Aruch (OC 53:6): We appoint to be Shali'ach Tzibur only one whose beard filled out, due to Kevod Tzibur.

Beis Yosef (DH uv'Seder): Rav Amram Gaon brings from R. Natrunai that the Gemara means that the ideal Mitzvah is to appoint one whose beard filled out. He is preferable over a youth. Surely, in a case or Bitul Kedushah, Baruch [Kevod Hash-m mi'Mkomo] and Yimloch and Amen Yehei Shmei Raba [of Kaddish], even a boy 13 years and one day may be Shali'ach Tzibur if it is impossible [to find someone older]. One who is not obligated in a matter may not exempt others (Rosh Hashanah 29a), for he is exempt from Mitzvos. A boy 13 years and one day is fine. The Rambam says that it is due to Kevod Tzibur. Therefore, if the Tzibur wants to pardon their honor, they may.

Beis Yosef (DH v'Chasav): The Kolbo (11, 8b) says that the lower beard must fill out. The Poskim said Stam "his beard filled out", which connotes the upper beard.

Beis Yosef (DH veha'Tosfos): Tosfos (Chulin 24b DH Nismalei) says that the Beraisa discusses being a fixed Shali'ach Tzibur to pray on fasts and Ma'amados. This connotes that he may be Shali'ach Tzibur the rest of the year. However, in Sukah (42b DH ha'Yode'a) Tosfos wrote that Chulin discusses being fixed Shali'ach Tzibur, and to pray on Yom Kipur, fasts and Ma'amados. This is like the Rosh, Rashba and Ran.

Taz (2): The Beis Yosef says that according to the Rambam, the Tzibur can pardon their honor, but not according to the Rosh. I say that surely the Rambam agrees that they cannot! Here, Kevod Tzibur is Kevod Shamayim. We honor Hash-m through a Shali'ach Tzibur proper to advocate on behalf of the congregation. We may not read [the Torah in the Beis ha'Keneses] from a single Chumash [rather, only from a full Sefer Torah], due to honor of the Tzibur (Gitin (60a). In Siman 143, the Poskim Stam forbid reading from a Chumash b'Tzibur. They didn't mention Kevod Tzibur. If pardon helps, they should have said that it is due to Kevod Tzibur, to teach that pardon helps! Rather, pardon does not help in these matters that pertain to Kevod Shamayim.

Magen Avraham (9): "Due to Kevod Tzibur" connotes that the Tzibur may pardon this. However, the Shulchan Aruch concludes "the Tzibur may not appoint..." I.e. it is forbidden even if they pardon. Also the Bach says so. In any case, l'Chatchilah one may not do so. Regarding fasts, we require one who is truly old (579:1), unlike Tosfos in Megilah, who connotes that it suffices that his beard filled out.

Kaf ha'Chayim (39): This refers only to fasts for rain. Other fasts are not so stringent.

Mishnah Berurah (24): This is for the rest of the year. On fasts, Rosh Hashanah and Yom Kipur, one may not appoint even haphazardly one without a full beard. Even pardon of the Tzibur does not permit.

Bi'ur Halachah (DH Aval): The Ran and Ramban permit only when there is no one else. The other Rishonim did not discuss this. It seems that the Shulchan Aruch is unlike the Ran, for in such a case he may even be a fixed Shali'ach Tzibur (Sa'if 7, Levush)! Also Ma'amar Mordechai permits occasionally even when there is someone else. However, one can dispel the proof. In Sa'if 7, we know that the entire year there will not be a fixed Shali'ach Tzibur with a full beard. Therefore, we may appoint a 13 year old even on a fixed basis. We may not do so Stam, for perhaps a fixed Shali'ach Tzibur with a full beard will be available.

Bi'ur Halachah (DH Yuchal): The Pri Megadim says that even an Avel may not be a fixed Shali'ach Tzibur without a full beard. One may be lenient for Ma'ariv, since there is no Chazaras ha'Shatz, just he says Kaddish and Borchu. The Rambam distinguishes between Prisas Shma and descending in front of the Teivah. The Lechem Mishneh says that he does not distinguish between fixed and occasionally. Also Bahag says so. Presumably, the Tzibur pardons [their honor] to the Avel, so we may join the opinion of the Beis Yosef and Shiltei ha'Giborim who are lenient about this.

Mesores Moshe (OC 58): Ha'Gaon R. M. Feinstein Ztz"l was asked about an Avel 14 years old, and preferred him for Shali'ach Tzibur over a Ba'al ha'Bayis, for he has less Aveiros.

Shulchan Aruch (ibid.): From when he brings two hairs, he may descend in front of the Teivah occasionally.

Beis Yosef (DH v'Ein): The Kolbo (11, 8:3) brings that R. Noson require two hairs that can be bent back to their source. If not, he is not called a man. We require a man for Tefilah, for it says "Madu'a Basi v'Ein Ish." The Rashba (Chulin 24b) said that it is not proper to appoint one without a full beard to be a fixed Shali'ach Tzibur, due to Kevod Tzibur. This is why in Chulin it says proper to be Shali'ach Tzibur, and did not say Kosher or he descends in front of the Teivah. In Megilah it says "he does not [descend] until he brings two hairs."

Beis Yosef (DH umi'Divrei): The Tur and Meforshim connote that a minor may not be Shali'ach Tzibur even occasionally. Why is the custom that minors are Shali'ach Tzibur on Motza'ei Shabbos? Perhaps Chachamim were particular only about Shacharis, which has Kedushah in Birkas Yotzer Ohr and Tefilah, and the Shali'ach Tzibur must repeat Shemoneh Esre to be Motzi the Rabim. A minor is not obligated, so he cannot be Motzi them. The Avudraham denounced the custom. Mahari Di Le'on tried to abolish it. The Rashba (Teshuvah 239) brought from the Ra'avad that since Berachos and Tefilos are mid'Rabanan, one might have thought that the mid'Rabanan Mitzvah of a minor who reached Chinuch can be Motzi a Chiyuv mid'Rabanan [of adults]. The Mishnah refutes this. It would be a disgrace for a minor to be Motzi the Tzibur. Based on this, we can justify the custom, and say that the Tzibur pardons their honor. Even according to Rashi, who says that it is because one who is exempt cannot be Motzi the Rabim, we can say that Ma'ariv is different, for it is Reshus (optional)

Magen Avraham (10: If he reached 13 years, we are not particular about [checking for] hairs, like [the Rema] says in 55:5.

Mishnah Berurah (25): We need not check for hairs. For a matter mid'Rabanan, we rely on the majority, who bring hairs [right after 13 years]. The Pri Megadim says that according to the Rambam, who holds that Tefilah is mid'Oraisa, a Shali'ach Tzibur may not be Motzi others unless we Vadai know that he brought two hairs.

Shulchan Aruch (ibid.): He may not be appointed by the Tzibur or a Shali'ach Tzibur who appoints him to lighten his responsibility and pray in place of him at known times.

Beis Yosef (DH Aval): The Rosh (Teshuvah 4:17) says that one without a full beard may pray [for the Tzibur] occasionally, like a city resident, who prays when he desires, as long as he is not appointed by the Tzibur or a Shali'ach Tzibur who appoints him to pray in place of him at times. The Tur brought this. It connotes that we may not appoint him even if the Tzibur pardons their honor.

Taz (4): The Tzibur may appoint him to be ready to pray when there is no Chazan in the Beis ha'Keneses. This is not called fixed at all, for perhaps it will never occur. Chachamim forbade only when there are fixed times when Vadai the youth will be Shali'ach Tzibur.

Mishnah Berurah (26): The Bach and Eliyahu Rabah say that even this (appointment to pray when there is no Chazan) is called fixed, and is forbidden.

Kaf ha'Chayim (47): In some places, during the week the fixed Shali'ach Tzibur has no beard, just the Shali'ach Tzibur for Shabbos has a beard. This is wrong.

Shulchan Aruch (8): If one clearly reached the age to have a full beard, we may appoint him even if he has no beard.

Kaf ha'Chayim (38): One who shaves his beard should not be appointed.