Gemara

(Mishnah - R. Yochanan ben Gudgada): If a father was Mekadesh his deaf daughter (before Bagrus), her husband can divorce her;

If an (orphaned) minor married a Kohen, she may eat Terumah.

Question: This implies that a deaf wife of a Kohen may not eat Terumah. What is the reason?

Answer: This is a decree lest a deaf wife of a deaf Kohen will eat.

Question: What is the concern? Beis Din is not commanded to stop a (Cheresh, who is like a) minor from eating (or doing any other) Isur!

Answer: This is a decree, lest a healthy wife of a deaf Kohen eat Terumah mid'Oraisa.

Yevamos 113b: R. Yitzchak bar Bisna lost the keys to the Beis Medrash in a Reshus ha'Rabim on Shabbos. R. Pedas said that they should get minors to play there. If they find the keys, they will bring them. He holds that if a minor is eating Isur, Beis Din need not stop him.

Question (Mishnah): If a minor comes to extinguish a fire on Shabbos we tell him not to, since we are commanded that he rest on Shabbos.

Answer (R. Yochanan): It is forbidden when the minor does so to please his father.

Support (Beraisa): If the son of a Chaver (one trustworthy about Ma'aser) often goes the house of his mother's father, an Am ha'Aretz, we are not concerned lest they feed him Tevel. If the Chaver finds food in his son's hand, he is not responsible.

Rejection (R. Yochanan): This is no support. We are more lenient about Demai (doubtfully tithed produce).

Question: This implies that if it was definitely Tevel, he would need to Ma'aser it. Above, R. Yochanan answered 'he does so to please his father' (but we need not stop minors who transgress for their own benefit)!

Answer: R. Yochanan is in doubt what is the Halachah. He rejects the proofs for both opinions.

Rosh Hashanah 32b (Mishnah): We do not stop children from blowing a Shofar (on Rosh Hashanah). We engage with them until they learn.

Beraisa: Even on Shabbos we encourage children to blow, until they learn. We do not stop children from blowing on Shabbos, all the more so on Yom Tov.

Question: The Reisha connotes that l'Chatchilah we tell them to blow!

Answer: The Beraisa distinguishes between children above and below the age of Chinuch.

Nidah 46a (Beraisa): The Torah considers a minor to be like an adult regarding "Lo Yachel Devaro".

He is like an adult regarding the Isur of Lo Yachel, but he is not lashed.

Question: In any case this is difficult! If Mufla Samuch l'Ish is mid'Oraisa (and it is forbidden even to him), he should be lashed. If it is mid'Rabanan, he should not be forbidden (Chachamim do not forbid minors)!

Answer: Chachamim commanded the one who supervises the minor to stop him from transgressing.

Inference: This shows that Beis Din is commanded to stop minors from transgressing!

Rejection (and Answer #2 to Question (b)): No. The case is, the minor was Makdish and adults ate it.

Rishonim

Rif (Rosh Hashanah 9b): On Shabbos we engage a child who reached the age of Chinuch to blow the Shofar. For a child below Chinuch it is permitted on Yom Tov, but not on Shabbos. Some say oppositely.

Ran (DH Omar): The Yerushalmi says that we permit a child who reached Chinuch. It is permitted on Shabbos only if it is Rosh Hashanah.

Rebuttal (Ri, brought in Rosh, Rosh Hashanah 4:7): Why do we permit a child who reached Chinuch? It is not a Mitzvah today. How can we tell him to do an Isur? And if a child is below the age of Chinuch, why can't we tell him to blow? We permit even an older child! (Rather, we permit a child below Chinuch.) In any case we need not stop him, since if it would not be Shabbos it would be a Mitzvah. When it says that we engage with him, it means that we let him engage. The Gemara (Erchin 2b) proves that 'everyone is obligated in Shofar' includes children from our Mishnah which says that we do not stop children from blowing.

Question: Why must we stop younger children? We need not prevent a minor from transgressing!

Answer (Ran DH v'Hani): We need not stop minors if the matter will not become known and lead to transgression. Here, people will hear the Teki'os, and (adults) might come to blow on Shabbos (outside of Beis Din).

Ran (Shabbos 1b DH Omar): They did not blow a Shofar in the Mishkan. It is a mere weekday action, and it is permitted when there is a need. This is why we encourage children to blow. A proper Shevus is not permitted even for the Mitzvah itself! This is unlike the Ramban, who says that it is a proper Shevus.

Rambam (Hilchos Ma'achalos Asuros 28): Even though Beis Din is not commanded to stop a minor from transgressing, his father must rebuke him and separate him in order to train him in Kedushah - "Chanoch la'Na'ar Al Pi Darko".

Magid Mishneh: If he father does not rebuke him, Beis Din is commanded to invigorate the father to rebuke his son to stop him.

Rashba (brought in Nimukei Yosef 42a DH Garsinan): This is reasonable. Since we train him to do Mitzvos, surely we must prevent him from Isurim! However, regarding a Mufla Samuch l'Ish (a minor shortly before adulthood) the Gemara suggested that Beis Din is commanded, and rejected this (Nidah 46b) Perhaps Chinuch applies only to Mitzvos Aseh, but not to Lavin!

Rambam (Hilchos Shofar 2:7): We do not stop minors below the age of Chinuch from blowing a Shofar on Shabbos that is not Rosh Hashanah, in order that they will learn. Adults may encourage minors of any age to practice on Yom Tov, since Teki'ah is forbidden only mid'Rabanan.

Poskim

Shulchan Aruch (OC 343:1): If a minor is eating Neveilos, Beis Din is not commanded to stop him, but his father must rebuke him and separate him (Rema - from an Isur mid'Oraisa). One may not feed him even an Isur mid'Rabanan.

Gra (DH v'Afilu): We may not be Me'arev with Tevel mid'Rabanan, for even minors may not eat it. The Rashba permits feeding an Isur mid'Rabanan to minors, but not consistently, lest the child continue to do so after maturing.

Magen Avraham (1): Beis Din is commanded to stop a minor if it will cause ruin, e.g. if adults hear him blow a Shofar on Shabbos, and they will do similarly.

Mishnah Berurah (5): If the child is sick and needs an Isur mid'Oraisa such as Chametz b'Pesach, one may tell a Nochri to feed it to him.

Kaf ha'Chayim (15): In every case it is better that a child eat Kosher food, for Tamei food can harm the child.

Aruch ha'Shulchan (7): Beis Din is not commanded to stop a minor, i.e. they need not check whether or not he does so for his father.

Teshuvas Shivas Tziyon (4 DH Emnam): The Magid Mishneh (Hilchos Shabbos 20:7) says that one may not feed Isur to a Cheresh. I know of no source for this. We cannot learn from a minor, for he will be obligated in Mitzvos. The Gemara asked why a Chereshes cannot be married to her sister's Pike'ach husband (Yevamos 114b), and why we don't give Terumah to a Chereshes married mid'Rabanan to a Kohen (Gitin 55a), since Beis Din is not commanded to stop minors. In both cases a Pike'ach makes a Chereshes transgress!

Rebuttal (Kaf ha'Chayim 8,21): R. Yerucham and several Acharonim forbid feeding Isur to a Cheresh. Even though Chinuch does not apply to a Cheresh or Shoteh, for he will never be obligated in Mitzvos, we may not feed to him Isur.

Rema: Some say that this refers to a minor below the age of Chinuch, but once he reached Chinuch we must stop him.

Beis Yosef (DH v'Chosvu): Tosfos and the Rashba say that if a child reached Chinuch, all the more so we must stop him from Isurim! We do not distinguish the father from Beis Din. However, the Rashba asks from places where we permit even a minor past the age of Chinuch. The Rambam holds that Beis Din never needs to stop a minor, but his father must stop him if he reached Chinuch.

Beis Yosef (DH ul'Inyan): The Ran (Yoma 1a DH Yom) permits feeding an Isur mid'Rabanan to a minor if it is for his needs. The Rashba said so l'Halachah, but not l'Ma'aseh. The Rambam forbids.

Mishnah Berurah (6): The Chayei Adam says that if he reached Chinuch we must stop him from an Isur mid'Oraisa. Only his father must stop him from an Isur mid'Rabanan.

Rema: Some say that Chinuch applies only to the father, not to Beis Din.

Mishnah Berurah (1): Some say that also the mother is obligated to be Mechanech her children.

Mishnah Berurah (3): One must not allow his children to speak Lashon ha'Ra, Rechilus and to swear, for he will get used to this and it will be very hard for him to refrain when he matures. The age of Chinuch in Lavin is when he understands that something is forbidden. Below this age a father need not stop him even from Isurim mid'Oraisa, but one may not feed Isur to him.

Mishnah Berurah (9): Beis Din must stop him from every Aveirah Bein Adam l'Chavero. However, the child need not pay for damage. It is proper that he go beyond the letter of the law and pay.

Shulchan Aruch (YD 373:1): Just like a Kohen is commanded not to become Tamei, adults are commanded about minors.

Be'er Heitev (1): The Agudah says that one need not wake a minor sleeping on Ohel ha'Mes, but it is good to do so for Chinuch. This does not apply to an infant without Da'as who needs his mother.

Question (V'Shav ha'Kohen Sof 56, cited in Pischei Teshuvah 1): The Rambam says that Tum'as Kohanim for relatives is permitted due to Aveilus. A minor is exempt from Aveilus. Is he therefore forbidden to be Metamei for relatives? Or, perhaps Chinuch does not apply to something that will be permitted when he is an adult!