Gemara

(Beraisa) R. Akiva: Nidah is a two-way Isur. She is forbidden just like he is!

R. Eliezer: Relations with a Nidah who is a minor is a one-way Isur. Only he is forbidden.

Gitin 45b (Rav Hamnuna - Beraisa): A Sefer Torah, Tefilin, or Mezuzah written by a minor is Pasul.

"U'Kshartam (you will tie)... u'Chsavtam (and you will write)" teaches that only one who is commanded to wear Tefilin is Kosher to write them.

Chulin 2a (Mishnah): If a Cheresh, lunatic or minor slaughtered while others looked on, the slaughter is Kosher.

12b (Rava): This is like R. Noson, who does not require intent for Shechitah of Chulin.

(Oshiya Ze'ira of Chavriya): The Halachah follows R. Noson.

Gitin 22b (Mishnah): Anyone can write a Get, even a Cheresh (deaf-mute), lunatic or minor.

(Rav Huna): This is when an adult supervises them.

Rishonim

Rosh (Chulin 1:4): The Mishnah discusses before the age of Chinuch (training in Mitzvos), i.e. when he can train his hands. If the minor is an expert and trained his hands, he may slaughter l'Chatchilah.

Hagahos Ashri: Even if the minor is an expert and trained his hands, if no adult supervised, the slaughter is Pasul.

Teshuvas Rosh (4:21): A minor cannot exempt others in Birkos Kri'as Shema. Even if he reached the age of Chinuch, he is obligated only for Chinuch.

Tosfos (Berachos 16a DH v'Rebbi): Chachamim hold that a minor can be Motzi adults (e.g. in Birkas ha'Mazon) when his Chiyuv is mid'Rabanan for only one reason, i.e. he is a minor. Megilah is mid'Rabanan even for adults, so there are two reasons why it is mid'Rabanan for a minor. Therefore, he cannot exempt adults.

Ramban (Kidushin 31a DH va'Ani): The minor is not obligated even mid'Rabanan. His father has a Mitzvah to be Mechanech him.

Teshuvas Maharil (196): If a Cheresh or lunatic fathered a child, surely he was Yotzei Peru u'Rvu. If you would say that he is like an animal, his Shechitah would be like that of a Nochri or monkey, even with supervision.

Turei Even (Megilah 24a DH Eino): Even though a minor is not obligated even mid'Rabanan (the Mitzvah of Chinuch is upon his father), R. Yehudah holds that Reshus (an optional Mitzvah) can exempt one who is obligated.

Terumas ha'Deshen (62): Even a minor who reached the age of Chinuch is not liable at all, even a moment before he brings two hairs. If a Zar became an adult on Shabbos, the Isurim of Avodas Zar and Melachah on Shabbos take effect on him at the same time (Yevamos 33a). Also, Beis Din need not stop a minor from eating Neveilos. If a minor wounded or damaged he is exempt, even when he matures, for he is not liable to punishments (Rosh Bava Kama 8:9). We derive that Mitzvos and Chukim do not apply to anyone exempt from punishments.

Nimukei Yosef (Yevamos 42a DH Garsinan): The Rashba says that since we train minors to do Mitzvos, surely we must prevent them from Isurim! However, the Gemara concluded that Beis Din is not commanded about a Mufla Samuch l'Ish. Perhaps Chinuch applies only to Mitzvos Aseh, but not to Lavin! The Ritva forbids feeding an Isur mid'Rabanan even to a minor below Chinuch.

Mishneh l'Melech (Hilchos Ma'achalos Asuros 17:27): Even if Mufla Samuch l'Ish is mid'Oraisa, the minor is not commanded

Kovetz Shi'urim (Bava Basra 413): The reason a minor is not punished is not because he is not commanded. Rather, even if he is commanded, he is not punished.

Poskim

Shulchan Aruch (YD 1:5): L'Chatchilah, we do not give animals to slaughter to a Cheresh, lunatic or minor who did not train his hands to slaughter, even if an adult supervises. If he slaughtered with supervision, it is Kosher.

Rema: He is called a minor until 13 years.

Levush (5): Some disqualify the Shechitah of a minor even if he knows the laws of Shechitah, until he is Bar Mitzvah. Since he did not reach a Chiyuv Shechitah mid'Oraisa, we do not rely on him l'Chatchilah. If an adult supervises it is l'Chatchilah if the minor is skilled, even if the adult does not know the laws, for the minor acts based on the adult who commands him.

Rebuttal (Tevu'os Shor 49): The Mishnah says that the problem with a minor is lest he ruin the Shechitah. This implies that he is a Bar Zevichah! If he slaughtered by himself, it is a Safek (Chulin 86a). According to the Levush, it is not a Shechitah at all! Perhaps in the Mishnayos (2a and 86a), an adult commanded the minor to slaughter, and he left. Alternatively, the adult does not know Hilchos Shechitah (and would not know if he paused or pressed...), therefore it is called 'by himself.' However, the Poskim do not say that an adult's command helps if the minor is not Bar Zevichah. No one says that supervision enables a minor to write Tefilin. In Avodah Zarah (27a) we tried to prove from Tziporah that a woman can circumcise. If a command helps, there is no proof! If a minor slept with an animal b'Mezid, there is Takalah (sin), just the Torah had mercy (and does not punish him - Sanhedrin 55b).

Shach (27): Surely a minor is commanded, since he may not eat without Shechitah.

Pischei Teshuvah (YD 11): The Magen Avraham (below) says that we may not rely on a boy to write Tefilin after 13 years until we check for hairs, for this is a Pesul mid'Oraisa. For mid'Rabanan laws, we rely on Rava's Chazakah. If so, here he may not slaughter after 13 years, either for the reason of the Levush (that he is not a Bar Zevichah), or the Shach's reason (he cannot testify if no one supervises), unless we check for hairs or know that he is 35 years old. From 13 years he may slaughter in order to feed to dogs, or with supervision even if he does not have skilled hands.

Shulchan Aruch (OC 39:1): If a minor wrote Tefilin, even if reached the age of Chinuch, they are Pesulim, for it says "u'Kshartam... u'Chsavtam." Only one who is commanded to wear Tefilin is Kosher to write them.

Beis Yosef (DH Tefilin): The Mordechai disqualified Tefilin that a minor wrote, even if he reached the age of Chinuch, for mid'Oraisa he is not commanded to wear them.

Magen Avraham (1): Since we learn from a verse, he must be a proper adult, i.e. he brought two hairs after 13 years.

Noda bi'Yehudah (2 OC 1): The Magen Avraham's Chidush is that we do not say that there is a Chazakah that once he reached 13 years, he brought hairs. The questioner wanted to support the Magen Avraham from the Mordechai, who disqualifies even a minor who reached the age of Chinuch. Ba'al ha'Itur says that Chinuch for Tefilin is from 13 years (without two hairs). If the Mordechai holds like Ba'al ha'Itur, this is explicitly like the Magen Avraham! Actually, in Hilchos Tefilin the Mordechai says 'a minor is Pasul because mid'Oraisa he is not obligated to wear Tefilin, unless he is 13 years old. In Erchin (3b)), we say that all are obligated in Tefilin, to include a minor who knows how to guard (Kedushas) Tefilin. Rashi says that this is mid'Rabanan.' This explicitly shows that the Mordechai holds that Chinuch is before 13 years.

Noda bi'Yehudah: We hold that what a Nochri slaughters is Nevelah. The Rambam learns from "v'Kara Lecha v'Achalta mi'Zivcho." The Ri and Rosh learns from "v'Zavachta v'Achalta" that you may eat what was slaughtered by a Bar Zevichah (one who eats only slaughtered meat). This is like Tefilin. A Mishnah is explicitly Machshir what a minor slaughtered if adults supervised. Why is a minor considered a Bar Zevichah, but not a Bar Keshirah (one who is commanded to wear Tefilin)?

Hagahah: Perhaps writing Tefilin requires intent, but Shechitah does not!

Noda bi'Yehudah: We must say that even though Beis Din need not separate a minor eating Nevelah, his father is obligated to separate him, due to Chinuch.(OC 343:1). Therefore, he is called Bar Zevichah. Likewise, if he reached Chinuch for Tefilin, he is Bar Zevichah.

Hagahah: Perhaps "u'Kshartam" applies to only to one who is obligated to wear Tefilin. There is no Chiyuv on a minor, only on his father. V'Zavachta is not a Chiyuv on any Yisrael. It is merely to permit the meat. We can say that this Mitzvah applies to the minor, for Beis Din stops him from eating meat without Shechitah.

Hagahah: The Shach said that a minor is commanded. This is difficult. We never find that he is commanded, just Beis Din are commanded to separate him. The Pri Megadim (OC Petichah Klalis 2:3) suggested that the Torah totally exempts minors only from Mitzvos Aseh, but they are obligated in Lavin, just they do not have Da'as (therefore they are not punished). The Maharil says that a Cheresh and lunatic are Bnei Mitzvah. If not, their Shechitah would be Nevelah, even with supervision. He did not mention a minor. Tevu'os Shor brings from Sanhedrin that a minor transgresses if he violates Torah law. In any case we can answer the Noda bi'Yehudah's question. "U'Kshartam" does not apply to minors at all, but v'Zavachta applies to him, for he may not eat Nevelah or Ever Min ha'Chai, like the Shach says. A Nochri may eat no matter how it died. He has no need for Shechitah.

Noda bi'Yehudah: The Rashba holds that Chinuch is only for Mitzvos Aseh. If so, a father has no Mitzvah of Chinuch regarding Nevelah, but he has regarding Tefilin. This is unlike the Mordechai. However, even though Beis Din need not stop him (from eating Nevelah), we may not feed it to him. Therefore, Shechitah applies to him more than Tefilin does.

Gra (DH Afilu) Even though he is obligated in Tefilin after reaching the age of Chinuch, this is only mid'Rabanan. Chinuch is mid'Rabanan, and this is a Pesul mid'Oraisa, for we learn from a verse.

Mishnah Berurah (1): The same applies to a Mezuzah.

Mishnah Berurah (2): Since this is mid'Oraisa, he is Pasul until his beard fills out, i.e. there are many hairs, even if they are very small, or until he lives most of his years (36). One should rebuke scribes who allow youths to write Tefilin without checking whether they brought Simanim of adulthood.

Mishnah Berurah (3): If we checked a boy above 13 and found that he has two hairs, we assume that he had hairs at the time he wrote.

Mishnah Berurah (4): It does not help if an adult supervises that he writes Lishmah.

Shulchan Aruch (186:2): A minor is obligated mid'Rabanan (to say Birkas ha'Mazon), to train him in Mitzvos. We say that a son may bless for his father, i.e. when the father did not eat to satiation, and is obligated only mid'Rabanan.

Mishnah Berurah (7): If the minor was not satiated, some say that he cannot be Motzi even an adult obligated mid'Rabanan. One should be stringent.

Kaf ha'Chayim (10): Some say that if a minor has no father, Chinuch applies to Beis Din. Others disagree. One should not be Yotzei from such a minor.