Gemara

155b (Mishnah): If Pa'utos (mature children) buy or sell Metaltelim, it is valid.

157a (Beraisa - R. Meir): R. Eliezer says, we can be Mezakeh for an adult, but not for a minor (who could not acquire for himself);

R. Yehoshua says, we can be Mezakeh for an adult, and all the more so for a minor!

R. Yehudah says, R. Eliezer says that we can be Mezakeh for a minor, but not for an adult, and R. Yehoshua says that we can be Mezakeh for a minor, and all the more so for an adult!

Gitin 59a (R. Yochanan): This was so they can buy Kedei Chayav (life essentials).

Question: What is the largest error that does not invalidate transactions of Pa'utos?

Answer (R. Yonah): They may err up to a sixth of the value, like for an adult.

Question (Abaye): Can Pa'utos give gifts?

Answer #1 (Rav Yemar): They cannot.

Answer #2 (Mar bar Rav Ashi): They can. This is whether the child is healthy or Shechiv Mera (sick and fears lest he die), whether the gift is large or small.

Kesuvos 70a (Rafram): If Pa'utos have an overseer, their sale is invalid.

Rishonim

Rif and Rosh (Gitin 27b and 6:23): The purchase and sale of Pa'utos are valid.

R. Chananel (citing Rav Hai Gaon, brought in Rosh, ibid.): We asked whether or not Pa'utos can give gifts (regarding the Mishnah Gitin 59a, which discusses) when there is no overseer (in which case they can sell). This implies that that when they cannot sell, obviously they cannot give.

Rejection (Rosh): This is not a proof. When there is an overseer, he buys and sells for them, therefore they cannot. An overseer may not give gifts! People give gifts only because someone pleased them. Therefore, Pa'utos can give even when there is an overseer (in order that others will do favors for them).

Hagahos Ashri: Children cannot sell or give land that they inherited until they are 20 years old.

Rosh (Gitin 5:19): Rav Hai Gaon says that Chachamim enacted that Pa'utos can buy and sell Kedei Chayav. Rav Hai adds that if there is much money, it seems that we give them a little merchandise so they can learn business, even though this is not essential. The Ramban says that once Chachamim enacted that Pa'utos can buy and sell, they can buy and sell anything. They can give gifts, even though this is not Kedei Chayav, in order that people will do favors for them. The Sugya of money entrusted to a third party also connotes that Chachamim did not limit the enactment.

Mordechai (Gitin 397, brought in SMA CM 235): We find that Chachamim permitted other things for the sake of livelihood, e.g. bread of Nochrim and lending to Nochrim on interest, even more than is needed for livelihood.

Rivash (109, brought in Beis Yosef CM 235 DH u'Mah she'Chosav b'Shem): The Rambam and others equate gifts to sales. Just like he cannot sell even Metaltelim when he has an overseer, he cannot give. The Rambam holds that he can give with the overseer's consent, even though the overseer himself cannot give.

Rambam (Hilchos Mechirah 29:6): Until six years, a child cannot be Makneh anything to others. From six until adulthood we check him. If he understands buying and selling, his purchase, sale and gift of Metaltelim are valid, for big and small matters.

Poskim

Shulchan Aruch (CM 235:1): A minor cannot sell or give land until he matures (13 or 12 for a boy or girl, with two hairs), even if he received the land for a gift, or the overseer bought it for him.

SMA (12, and Drishah 10): If a minor himself bought land, since he can demand his money back it is like Metaltelim, and he can sell or give it.

Even if the child gave it through a Matanas Shechiv me'Ra, even if he was given the land, it is void, even if he is proficient about buying and selling.

SMA (13): Chachamim enacted special powers of Matanas Shechiv me'Ra, lest anguish (over inability to give a gift) precipitate death. One might have thought that for this reason, even a minor can give land. There is no Mitzvah to fulfill the words of a deceased minor.

Rema: However, as long as the child is happy with his sale, and his relatives or Beis Din did not annul his act, and the buyer ate the produce of the land he bought, he need not pay for what he took.

SMA (14): The (Rashba, attributed to the) Ramban (Teshuvah 2) says that a minor's sale is totally Batel. Even if he did not protest, his relatives or Beis Din can remove the buyer from the land. If the minor went away, the buyer may not eat the Peros. However, if the minor wants the sale to stand, and the buyer ate the Peros, we do not make them return them. Even if the minor retracts later and says that he thought that the gift was valid and he mistakenly pardoned the Peros, mistaken pardon in a sale takes effect. This is especially if the minor authorized him to eat. Pardoning Peros is like a gift (of Metaltelim), which is valid. The Rambam (Mechirah 29:17) and Shulchan Aruch (Sa'if 14) require the buyer to return the Peros. We can say that this is like the Ramban if the buyer did not eat in front of the minor, or if he ate in defiance of his protest. However, it seems that whenever the minor and his relatives are here and do not protest, this shows approval, and the buyer may eat.

Shulchan Aruch (ibid.): If he inherited a loan document from his father, it is like Metaltelim, and he can sell or give it to someone else.

Source: Rosh (85:10), cited in Beis Yosef (DH u'Mah she'Chosav b'Shem).

SMA (15): One might have thought that he cannot sell it, for documents are like land in most respects. The Ritva says that he cannot sell it because it is Mili (intangible), and it can be sold only through writing (another document) and handing it over, and Chachamim did not enact these for minors.