Gemara

(Mishnah): Anyone Kosher to judge is Kosher to testify.

Bava Basra 155b (Rav Huna brei d'Rav Yehoshua): An adult less than 18 (or 20) can testify.

(Mar Zutra): He can testify only about Metaltelim, but not about land.

Question (Rav Ashi): Presumably, you say that he can testify only about Metaltelim, because he can sell them. If so, even a minor should be able to testify about Metaltelim, for a Mishnah says that Pa'utos (mature children, from the age of six to 10 years) can buy or sell Metaltelim!

Answer (Mar Zutra): It says (about witnesses) "v'Omdu Shnei ha'Anashim." Minors are not men.

Shabbos 56b (R. Shmuel bar Nachmani): If one says that Yoshiyahu sinned, he errs - "va'Ya'as ha'Yashar b'Einei Hash-m". "...Asher Shav" does not mean that he sinned and repented. Rather, he overturned every judgment that he made from the age of eight until 18. He did not take back the money from the one to whom he gave it. Rather, he did this "b'Chol Me'odo" (from his own money).

Rav disagrees, for he said that Yoshiyahu was the greatest penitent of his generation.

Nidah 46a (Rava): A girl may not do Mi'un after 12 years, for she is Muchzekes to be an adult.

Rishonim

Rif (Bava Basra 73b): Rav Huna taught that a 13 year-old can testify, even if he does not know about business, even though he cannot buy or sell. Mar Zutra said that this refers only to Metaltelim. Minors cannot testify, for it says "v'Omdu Shnei ha'Anashim."

Rambam (Hilchos Edus 9:8): If a 13 year old has Simanim above, we need not check him. If not, we do not accept his testimony until he is checked.

Rambam (Hilchos Ishus 2:15): If a boy above 13 did not bring a Siman below, and he brought all the Simanim above, it is a Safek whether he is a minor of adult. If he was not checked below, since he has Simanei Bagrus above, he is assumed to be an adult.

The Rosh (Bava Basra 9:34) brings the Gemara in Bava Basra.

Rashi (56b DH Ad) Yoshiyahu overturned every judgment that he made from the age of eight until the age of 18, when Chilkiyah found the Sefer Torah and Yoshiyahu realized that perhaps he erred.

Poskim

Shulchan Aruch (CM 7:3): Some say that a judge must be at least 18 years old with two hairs. Some say that a 13 year-old is Kosher even if he did not bring two hairs.

Maharsha (Shabbos 56b DH Kol): The Tur learned from here that a judge must be at least 18 years old. What is the source? The verse does not mention 18, only that he became king at the age of eight. The Gemara does not say until Ben 18 (like it said 'from Ben 8'), rather, until 18. It seems that it refers to until the 18th year of his reign, when they found the Sefer Torah. He was stringent to retract all his rulings.

Beis Yosef (DH Katan): The first opinion learns from (R.) Shmuel. The latter opinion is from the Yerushalmi. R. Yerucham says that it is primary.

Birkei Yosef (10): When the Shulchan Aruch brings 'some say... and some say...', he rules like the latter opinion.

Levush: A minor cannot judge because he is exempt from Mitzvos. If a 13 year-old is sharp and fluent in Torah law, he can judge with others, or alone, like an expert. Some forbid until 18 years even if he brought two hairs, for then he understands keenly the give and take between people. We find that Yoshiyahu retracted every judgment he made from when he became king until 18, for he did not consider them to be judgments.

SMA (8): An 18 year-old is a proper man with strength to save an Oni from his oppressor, which is a required trait of a judge.

SMA (9): Even though witnesses must have two hairs, that is because it says "ha'Anashim". Judgment requires only sharpness and knowledge. However, below 13 is Pasul, for he is not called an adult at all Even though anyone Pasul for testimony is Pasul for judgment, being too young disqualifies for both of them, each according to its Shi'ur.

Note: The Taz (35:1) says like the last words of the SMA.

Shulchan Aruch (CM 35:1): A minor cannot testify until he brings two hairs after 13 years. If he was not checked until long after 13 years, and he had two hairs, he is Muchzak to be an adult from 13 years. If has a full beard, we need not check him.

Source (Beis Yosef DH v'Im): Tosfos (Yevamos 80b d v'Hevu says so). The Tur brings this in EH 169. Here he calls it 'sprouting of the beard', which means a full beard. Why didn't he say a full beard, like he said there? Perhaps only there, for Chalitzah, we require a full beard. However, what is the source to distinguish? The Rambam (Hilchos Edus 9:8) says that if a 13 year old has Simanim above, we need not check him. However, he holds that the beard is a Siman.

Rebuttal (Gra 5): Tosfos connotes unlike this! Rather, the Tur learned from the Rambam (Hilchos Ishus 2:15).

SMA (4): The Gemara discusses a full beard. I.e. there are many hairs; they need not be as long as the Shi'ur for lower hairs. The Tur discusses sprouting of a beard. I say that this is the same.

Avnei Nezer (EH 215:17): Do not say that CM 35 discusses testimony to keep money, and as long as the witnesses were not checked, their testimony is void. Tosfos (Bava Kama 72b) says that even Rav Chisda, who says 'what good are Safek Pasul witnesses?!' agrees that their testimony enables one to avoid paying. The same applies to a Safek minor. Rather, CM 35 discusses testimony to obligate one to pay. Therefore, we do not rely on Chazakah d'Rava, which is based on a majority, for we do not rely on the majority for monetary matters.

Avnei Nezer (EH 215:17): Judgment depends on clear understanding. We do not equate the Pesulim of judgment and testimony to each other. A minor is Pasul for each, for its reason.

R. Akiva Eiger (Teshuvah 73): Even though we permit vows through relatives and at night, a judge to permit vows must be Kosher to judge other cases. If a woman cannot judge, she cannot permit vows. The same applies to a minor, according to Tosfos (Nidah 50a), who disqualifies him from judging. The Tur is Machshir, based on the Yerushalmi. I think that he refers to a minor whom we did not check; we rely on Chazakah d'Rava. Chachamim were stringent not to rely on this Chazakah for mid'Oraisa laws like Chalitzah. Since the Torah did not write 'Ish' to disqualify a minor from judging (like it wrote regarding witnesses), for judging we rely on the Chazakah. The SMA connotes that even a Vadai minor can judge, but the Bach says that before 13 years he is Pasul because we do not see adulthood in him. He does not say that he is a Vadai minor. This implies that if he is 13, and we checked and did not find two hairs, he can judge. However, the Beis Yosef explains that we hold that a woman cannot judge because we learn from testimony. We do not say that judgment depends on sharpness, and a sharp Chacham woman can judge! We should also disqualify a minor, just like for testimony, without distinction! The Tumim says so (that if we checked and did not find hairs, he is Pasul). One must check judges for Chalitzah. If so, we can say that also to permit vows, which is an Isur, we do not rely on Chazakah d'Rava, and one must check.