1. Minors when do they start to fast Young children are permitted in all these (Yom Kippur restrictions) except wearing (leather) sandals because we are not so worried if they do not wear them. Note (Rema): And it is permitted to say to a Gentile to wash them, to anoint them, but to feed them even with one's own hands is allowed [Tur].
2. A minor, who is healthy, that is 9 complete years old or 10 complete years old, we train him for hours. How so? If they are used to eating in the 2nd hour of the day, we feed them in the 3rd hour. If they are accustomed to eat in the 3rd hour, feed them in the 4th hour. According to the strength of the son, we add to the fast in hours. Parentheses (Rema): The same would be with a healthy female minor [Tur]. An 11 year old child whether male or female we have them fast and complete from Divrei Sofrim (the Words of the Scribes - meaning either Rabbinical or from Scripture besides Chumash) in order to train them in Mitzvos. Note (Rema): And there are those that say it is not necessary to complete Rabbinically at all [Ran, Or Zarua, Haagos Maimoni in the name of the Behag, Rokeach, and Ra'am]. And in all places we train in eating, we train in washing and anointing [Tur]. A daughter that is 12 and a day and a son who is 13 and a day that has 2 hairs (pubic, serving as determination of adulthood) are like adults for all mitzvos, and complete (the fast) from the Torah (i.e. their obligation is from the Torah). But if they do not have 2 hairs, still they are minors, and do not complete except from Divrei Sofrim. Note (Rema): And even if they are scrawny or weak, it is necessary to complete because we are concerned perhaps the hairs fell off [Terumas HaDeshen Siman 155]. A children who is less than 9 does not fast (at all) on Yom Kippur in order that they not come to danger. Note (Rema): Even if (the child) wants to be strict on himself, we actively protest [Kol Bo].