Gemara

31b (Mishnah): If Reuven sent an Eruv with a minor it is invalid.

Question: Rav Huna allows a child to collect the Eruv!

Answer: He permits this for Eruv Chatzeros. Our Mishnah forbids for Eruv Techumim.

58b (Mishnah): Even a male or female slave is believed to say 'the Techum extends to this place', for Chachamim enacted Techumim to be lenient, and not to be stringent.

Avodah Zarah 75b (Beraisa): If one buys from a Nochri a Kli used for food, it must be immersed in a Mikveh of 40 Sa'im.

(Rava): "... Ta'aviru ba'Esh v'Taher" obligates an additional Taharah after Kashering.

(Bar Kapara): "B'Mei Nidah" obligated immersing it in water that a Nidah could immerse in, i.e. a Mikveh of 40 Sa'im.

R. Yitzchak bar Yosef thought to immerse a Kli made of earth.

R. Ya'akov: The Parshah discusses only metal Kelim.

(Rav Ashi): Since glass Kelim can be [melted and] made again if they break, they resemble metal Kelim, and they require immersion.

Rishonim

Tosfos (31b DH Kan): We do not believe minors about Eruv Techumim, because a verse (an Asmachta) supports it. They are believed about Bedikas Chametz, i.e. in their own house, but not to be a Shali'ach for others. The Yerushalmi says that a minor is believed to be Me'arev for himself, but not for others.

Rivash (245): A minor is believed about mid'Rabanan laws to be lenient, but not to be stringent, if it is is b'Yado (within his power). What is not b'Yado, he is not believed to change its Chazakah, to permit or forbid.

Tosfos (Pesachim 4b DH Hemnuhu): Techumim is an Isur mid'Rabanan. We believe women and slaves for it (Eruvin 58b), but not minors. They are believed less. Here, [regarding who is believed about Bedikas Chametz], minors were taught after women and slaves. They are believed only because Bedikah is mid'Rabanan. Only after a minor matures, he is believed to say '[when I was a minor,] we used to go until here on Shabbos' (Kesuvos 28a). This is because it is not b'Yado at all, unlike Bedikas Chametz.

Tosfos (Chulin 12b DH Man): Shechitah of a minor is Pasul, even if others see him. Why does supervision enable a minor to write a Get? There, they teach him and admonish him to intend. Here, they merely see.

Terumas ha'Deshen (257): One may not send a minor to immerse a metal Kli bought from a Nochri. The Torah obligates immersing them, and a minor is not believed, even though it is b'Yado and it is not a toil. Tosfos (Pesachim 4b) says that women and slaves are believed about Torah Isurim, but not minors. Techumim is an Isur mid'Rabanan. We cannot learn to disqualify from Hagahos Ashri (Chulin 2:8), who requires a woman immersing from Nidah to intend to become permitted to her husband, even though this is Chulin. Tosfos (Chulin 12b) showed that if adults supervise and instruct a minor, we say that he has intent. One can instruct a minor to intend for Taharah, even without supervision [when he immerses the Kli]. Also, what is the source that this Tevilah requires intent? There is no previous Tum'ah, and the Kli does not forbid what is put in it before Tevilah. It is a mere Gezeras ha'Kasuv.

Poskim

Shulchan Aruch (YD 120:14): A minor is not believed about Tevilas Kelim.

Taz (16): The Rema did not say that the adult must instruct the minor. This connotes that he holds like the latter answer in Terumas ha'Deshen, that Tevilas Kelim does not require intent at all.

Gra (36): Most Poskim say that Tevilas Kelim is mid'Oraisa, like Avodah Zarah 75b. A minor is not believed about what is not b'Yado even for mid'Rabanan laws. In Pesachim, we say that women, slaves and minors are believed about Bedikas Chametz because it is mid'Rabanan. Because it is a toil, they would not be believed if it were mid'Oraisa, i.e. women and slaves. Minors are not believed about Torah laws in any case. Tosfos connotes like this.

R. Akiva Eiger: It seems that we believe minors about glass Kelim, for all agree that its Tevilah is mid'Rabanan (Pri Chodosh 3,26, Sha'agas Aryeh 56, Panim Me'iros 2:97). However, according to Tosfos (31b), for mid'Rabanan laws he is believed only about his own, but not to do Shelichus for others.

Mishbetzos Zahav (OC 451:6): This is difficult (believing minors about glass Kelim). It seems that he is not believed even for Tevilah of glass Kelim, which is mid'Rabanan, since there is Chezkas Isur (Rema YD 127:3)! However, if a child reached 13 years, we need not check for hairs to immerse glass Kelim. For metal, we can say that we must know [Vadai] that he is an adult.

Pischei Teshuvah (14): Perhaps even for metal, we need not know [Vadai] that he is an adult. Tevilas Kelim is lighter than other Torah Isurim. If one used the Kli before Tevilah, it does not forbid the contents (Rema, Sa'if 16). See what I wrote in 281:7 [about whether for matters such as writing Tefilin, one may rely on the Chazakah that a boy brings hairs right after 13 years].

Shulchan Aruch (ibid.): If they immersed in front of an adult, it is valid.

Gra (37): Even if the Kli fell in by itself, it is a good Tevilah. We do not need supervision. (It is only so we will know that he immersed it - PF.)

Rema (YD 127:3): In any case, if a minor is sharp and expert in a matter, if he testifies to be lenient about an Isur mid'Rabanan, and there is no Chezkas Isur, e.g. Bedikas Chametz, he is believed. Chachamim believed him about mid'Rabanan matters. If there was Chezkas Isur, he is not believed at all.

Gra (29): If a minor knows how to slaughter, one may eat from his Shechitah only if an adult supervised. The Ritva (Sukah 42b) explains that the minor is not believed to say that he slaughtered properly.

Gra (32, Likut): For what it is b'Yado to fix, women and minors are believed even about Torah laws, such as Shechitah and Taharos, unless it is a big exertion or there is a Safek or reasons to be lenient [lest they be overly lenient]. For mid'Rabanan laws, they are believed even for a big exertion or when there is a Safek or reasons to be lenient. If it is not b'Yado, a minor is not believed even for mid'Rabanan laws.

Rema (ibid.): A minor is not a witness to be believed for Isurim. However, if he is sharp and proficient in the matter, and there is supporting evidence for his words, one should be stringent if he testifies about Isur. Chachamim believed him to testify leniently about an Isur mid'Rabanan, such as Bedikas Chametz. If the Isur was Muchzak, he is not believed at all.

Shulchan Aruch (OC 437:4): If a house was Muchzak to be unchecked, and a (woman or) minor said 'I checked it', he is believed, if he has Da'as to check.

Magen Avraham (8): In Eruvin, Tosfos says that a minor is not believed to be a Shali'ach for others. In Pesachim, Tosfos says that he is believed about what is b'Yado even for Torah laws, but not for Bedikas Chametz (if it were mid'Oraisa), for it is an exertion. The Shulchan Aruch (YD 120:14) rules that a minor is not believed about Tevilas Kelim.

R. Akiva Eiger: Tosfos said only that women and slaves are believed for Torah laws! Also the Magen Avraham means like this. This is why he brought from YD that minors are not believed about Tevilas Kelim. Terumas ha'Deshen connotes that minors are believed about Tevilah of glass Kelim, which is mid'Rabanan, unlike Tosfos in Eruvin. I do not understand Tosfos' proof. There, the minor does not return and say that he fulfilled the Shelichus. The Mishnah teaches that we do not rely on the Chazakah that he did the Shelichus. Perhaps a minor is believed if he says that he did it! This requires investigation.

Magen Avraham (8):. The Rema is difficult. In YD 127:3 he says that Chametz is not considered Chezkas Isur, therefore a minor is believed. Chametz is Chezkas Isur, like the Rivash says! Rather, he is believed because it is b'Yado. The Beis Yosef (YD 120, citing Terumas ha'Deshen 46) connotes that according to the opinion that Tevilas Kelim is mid'Rabanan, a minor is believed about it.