This Halacha is an excerpt from our Sefer
All children who are above the age of Bar or Bas Mitzvah are obligated to fast on all accustomed fast days. All children who are below the age of Bar or Bas Mitzvah, are not required to fast any of the four Rabbinical fasts, including Tishe Beav. [This applies even if the child is within three fasts from his/her Bar/Bas Mitzvah. One is not even required to educate the child to fast for a certain amount of hours into the day [i.e. Taanis Shaos]. Nevertheless, some Poskim rule that regarding Tishe Beav, children who have reached the age of education in this regard, which is approximately nine years old, are to delay their meals a few hours into the day from its set time. However, children below the age of education are to be fed like normal and it is even forbidden to delay their meals from their regular times, being that this can lead them to becoming in a state of danger.]
What may the children eat? Some Poskim rule that a child which has reached the age of understanding the mourning is only to be allowed to eat bread and water or other simple staple food. The custom however is not like this opinion. [However, they are not to be given sweets and the like, although one is not required to stop them from eating it if they are in the midst of doing so.]
Are children to fast on the night of Tishe Beav until morning?
The custom of many is that children of Chinuch age fast until the morning. This is not required from the letter of the law.
If one is not fasting, is he to wash hands as usual [until the wrist] when eating bread on Tishe Beav?
If a child below Bar/Bas Mitzvah desires to fast on Tishe Beav, may the parent allow him to do so?
If the child is already close to the age of Bar/Bas Mitzvah and the parent does not see any danger involved for the child to fast, then although he may not force the child to fast, he is also not required to protest him from fasting.
When Tishe Beav falls on Sunday, are children who have reached the age of Chinuch to say Havdala prior to eating?
If a child became Bar Mitzvah on Sunday Tishe Beav Nidche, must he fast?
 Admur 616/9
 Admur 616/9; Elya Raba 549/7; Kaf Hachaim 550/1
Two hairs: The above law only applies if the child has reached puberty which means that he or she has grown two pubic hairs. If the child has reached this age but does not have two pubic hairs, then although he or she must keep all the commands out of doubt that perhaps he or she grew the hairs and they fell off, nevertheless the child is not required to fast any of the Rabbinical fasts. [Admur ibid]
Other Poskim: Some Poskim rule the child must fast even the Rabbinical fasts once he or she reaches 13/12 even if the child has not yet grown two hairs. [P”M 550 A”A 2; Biur Halacha 550 “Hakol”; Kaf Hachaim ibid]
 Admur 616/9; Elya Raba 549/7; M”B 550/5; Kaf Hachaim 550/1
 There is no source in Poskim for educating a child to fast the three fasts prior to his Bar/Bas Mitzvah. On the contrary, it is forbidden to force the child to do so, if they do not desire to fast. On the other hand, if they desire to fast, there is no need for the parent to stop them.
 Chayeh Adam 133/6; M”B ibid; Kaf Hachaim 550/9; Piskeiy Teshuvos 550 footnote 10
Other Opinions: Some Poskim rule that children [of nine years old] are to be educated to fast for a few hours into the day just as is the law on Yom Kippur, as rules Admur 616/5. [see Poskim in next footnote]
 Erech Hashulchan 554/2 and Beis Hillel brought in Kaf Hachaim 554/23; Siddur Yaavetz; Chanoch Lenaar 21 footnote 9; Beir Moshe 8/98; Piskeiy Teshuvos 554/9 that so is the custom; Nitei Gavriel 64/2
 Both boys and girls.
 Such as if they normally eat at 2:00 they are to eat at 3:00 and so on and so forth in accordance to the amount of delay that the child can handle. [Admur 616/5]
 Admur 616/10 regarding even Yom Kippur
 M”A 550/2; Rameh 111; P”M 549 A”A 7; Chayeh Adam ibid; M”B ibid; brought in Kaf Hachaim 549/8 and 550/9
 Some write this is starting from age nine. [See Piskeiy Teshuvos 550 footnote 11]
 Birkeiy Yosef 549/1; Daas Torah; Kaf Hachaim 549/8 and 550/9; Beir Moshe 8/95
 Beir Moshe ibid; Piskeiy Teshuvos 550/3
 Nitei Gavriel 64/1
 Kaf Hachaim 554/53 in name of Tosefes Chaim 155/10
 I have not found this explicit in the Poskim. However see Nitei Gavriel 64/2 for a similar ruling; See also Likkutei Dibburim, vol. 4, p. 1418 that the Rebbe Rashab allowed his son to fast on Yom Kippur from age seven!
 See Piskeiy Teshuvos 556/4
 Divrei Yatziv 243
 SSH”K 62/45; Nitei Gavriel 95/7
 Divrei Malkiel 5/130; Yad Sofer 7; See Yad Efraim on M”A 554/9
 Maharsham 3/363; Avnei Nezer 426; Mishneh Sachir 2/147
 Nitei Gavriel 64/5