Gemara

(Mishnah): If any of the Arayos had Bi'ah with a three year-old girl, he is killed, and she is exempt.

Suggestion: 'Any of the Arayos' includes an animal. It is killed, even though there is only disgrace, not Takalah (stumbling in sin)!

Rejection: Since she was Mezidah, there is also Takalah. The Torah had mercy on her (since she is a minor) and does not kill her.

Bava Kama 87a (Mishnah): Encounters with a deaf-mute, lunatic or minor are bad. One is liable if he damaged a minor, but a minor who damaged is exempt. Encounters with a slave or woman are bad. One is liable if he damaged one of them, but if (s)he damaged, (s)he pays only after freedom or divorce.

98b: A case occurred, and Rafram forced Rav Ashi to pay the full value of a loan document that he burned.

Shabbos 56b (R. Shmuel bar Nachmani): If one says that Yoshiyahu sinned, he errs - "va'Ya'as ha'Yashar b'Einei Hash-m."

Question: "...Asher Shav" connotes that he sinned and repented!

Answer: He overturned every judgment he made from the age of eight until 18.

Suggestion: Perhaps he took back the money from the one to whom he gave it!

Rejection: He did this "b'Chol Me'odo" (from his own money).

89b (R. Shmuel bar Nachmani): In the future, Hash-m will tell Yisrael 'your children sinned';

Yitzchak: Did my children sin? Aren't they also Your children?! ... Further, how much did they sin? Most people live only 70 years. Deduct the first 20, for which You do not punish. Fifty years remain...

Rishonim

Rambam (Hilchos Geneivah 1:10): It is proper for Beis Din to hit minors for stealing, according to the strength of the minor, so they will not be used to doing so. The same applies if they are used to other damages.

Magid Mishneh: I did not find this explicit, but it is obvious. Even though according to the opinion that Beis Din need not stop minors from eating Neveilos, this is only for Aveiros between man and Hash-m. Surely we must stop them from Aveiros between man and man, lest disaster result.

Migdal Oz: The Rambam learns from Bava Kama 96b (a man stole oxen, worked with them, then returned them. Rav Nachman said that the owner receives half the increased value. This was a fine, for the man stole many times. Beis Din may lash and punish unlike Torah law (Sanhedrin 46a).

Mordechai (Bava Kama 92): Encounters with a slave or woman are bad, for they do not pay for damage now. R. Nachshon Ga'on says that we lash them, lest slaves hit free men, and women hit men.

Rosh (Bava Kama 8:9): If a slave or woman damaged, he or she is liable after freedom or divorce. This is unlike a minor, who is not liable to punishment.

Or Zaru'a, in Hagahos Ashri: Rashi says that this is why Rafram forced Rav Ashi to pay. This shows that a minor is obligated to pay after he matures. Also, R. Yosi b'Ribi Chanina said that says when the minor grows up, the Apotropus collects from him for what his animal damaged (Bava Kama 39b). All the more so, after he matures he must pay for what he damaged!

Rebuttal (Bach OC 343 DH Ach): Also Bein Adam la'Makom there is no punishment after he matures. In any case, it is good to do Teshuvah by himself for all he transgressed when he was a minor, Bein Adam la'Makom or Bein Adam l'Chavero.

Taz (OC 343:2): Rafram verbally forced Rav Ashi to go beyond the letter of the law. We find that Rav ruled that Rabah bar bar Chanah must go beyond the letter of the law and pay workers who broke his barrel (Bava Metzia 83a).

Terumas ha'Deshen (62): The Rosh exempts if a minor who wounded or damaged, even when he matures, for he is not liable to punishments. This shows that Mitzvos and Chukim do not apply to anyone exempt from punishments. Bahag obligates him when he matures. The Gemara connotes that it is a bad sign if pitfalls came through a minor. Therefore, it seems that it is good if he accepts some atonement upon himself, also for one who transgressed his vow.

Poskim

Rema (OC 343:1): If a minor hit his father or transgressed any other Aveirah before adulthood, even though he does not need Teshuvah when he matures, it is good to accept upon himself some matter for Teshuvah and Kaparah, even though he transgressed before he was liable to punishments.

Magen Avraham (4): Sanhedrin 55b says that if a minor had relations with an animal, there is Takalah.

Gra (DH mi'Kol): We learn from Shabbos 56b and Rashi in Bava Kama.

Noda bi'Yehudah (2 YD 164): It is unreasonable to say that there is no punishment b'Yedei Shamayim before 20 years old. Is the world Hefker, that people below 20 may murder, be Megaleh Arayos and do all Aveiros when there are no witnesses?! Rather, Hash-m does not punish in this world before 20, but after death one will be punished for everything he did once he had Da'as, even from the age of Pa'utos, that he knew that it is an Aveirah. Yitzchak argued to spare Yisre'elim from punishment in this world. Even if one would say that even after death there is no punishment for Aveiros before 20, there is reward for Mitzvos before 20, and Aveiros block this.

Chasam Sofer (YD 155): When one needs a Kaparah, we do not distinguish whether or not he is above 20. A Bar Mitzvah is liable for all Chiyuvim in Beis Din above and below. According to the opinion that a Yoledes, Metzora and Nazir bring Chata'os because they sinned, you cannot say that one under 20 does not bring! Shevuos 8a asked for whom the inner goat of Yom Kipur atones. It cannot atone for idolatry b'Shogeg, for the sinner brings a Chatas. We did not say that it atones for people between Bar Mitzvah and 20! Medrashos say that Shamayim punishes only those above 20. This applies to new matters that arise, e.g. the punishment of Dor ha'Midbar. It says at 100, Sarah was like a girl of 20 regarding sin. (This is the text of the Medrash brought in Rashi Bereishis 23:1.) This Shi'ur applied before Matan Torah, when there was punishment only for Mitzvos of Sechel (intellect). All Shi'urim are a tradition from Moshe from Sinai. A 13-year old with Simanim is liable for all punishments.

Pischei Teshuvah (YD 185:9): Shabbos 89b connotes otherwise.

Chavos Ya'ir (166): The Zohar (Bereishis 291) says that when one dies 'b'Chet'o' (for his sin) before 20, Hash-m removes His Hashgachah from him, and the Mashchis itself kills him. He has no punishment b'Yedei Shamayim. If so, why does a 13 year-old bring a Korban? He would not get Kares if he were Mezid! I would distinguish between punishments in this world and the next, and between a Chet Bein Adam la'Makom and Bein Adam l'Chavero, but the Medrash that Rashi brings does not distinguish.