Child who caused damage:
If a child caused bodily damage to another person he is exempt from paying for damages even when he becomes older.
Doing repentance above the letter of the law: Even though one is exempt from paying for the damages, it is nevertheless proper for him to accept upon himself when a gets older a certain matter for the sake of repentance and atonement, even though he had transgressed before he became of punishable age. [He should therefore pay the owner for the stolen object. He however is not required to pay for the entire worth of the object, but rather a symbolic amount. Some however write that he should pay the owner for the entire amount, however seemingly this is only a Midas Chassidus. Whatever amount the owner receives, he should be kind and merciful to forgive the person for his childhood sin.]
Is a child who caused damage that is below the age of Chinuch encouraged to perform a certain matter for the sake of repentance?
Some Poskim rule that the above Teshuvah is only relevant for children who damaged when they were of age to remember what they did. If however they were of very young age, and they don’t remember the incident, they are not required to do Teshuvah at all.
Is the father of a child obligated to pay for his sons damages?
No. If however the father was negligent and was the direct cause of the damage then it is possible that he is liable to pay for damages.
 Michaber 424/8; Mishneh Baba Kama 87a “A child, getting into an altercation with them is bad, as if they damage they are exempt while if you damage them you are liable”
 The reason: As at the time that the damage was done they were not of an age of responsibility. [Michaber ibid]
 Admur 343/11; Rama 343; Mahariy 62; Bach 343; Shvus Yaakov 1/177 brought in Pischeiy Teshuvah C.M. 349/2; Based on story in Shabbos 56b; Baba Kama 98b, brought in Kaf Hachaim 343/32
Other opinions: Some Poskim rule that a child is not required to repent at all for his wrongdoing even when he becomes older. [Beis Yaakov 3, brought in Shvus Yaakov ibid] Practically, we do not rule like his opinion. [Shvus Yaakov ibid; Kaf Hachaim ibid]
 The reason: The purpose of this repentance is not for the sake of removing Divine retribution, being that he is not liable for any punishment. However the forbidden act, despite not being punishable, leaves a damaging impact and spiritual stain on the soul of the child. It is for this reason that the child should do some act of repentance for the sake of cleansing his soul of any spiritual blemish. [Bach 343: The verse in Mishlei 19/2 states that “Even without knowledge, a soul is no good.” This teaches us that even a child that transgresses a sin without knowledge causes impurity to his soul, it is thus proper for him to do Teshuvah”; Likkutei Sichos 14 p. 144 footnote 13; Sichos Kodesh Balak 5730; Shulchan Hamelech 343]
 Shvus Yaakov 1/177, brought in Pischeiy Teshuvah ibid; Kaf Hachaim ibid; Based on Admur an Rama ibid, based on Terumos Hadeshen 2/62
 Sefer Chassidim 692, brought in Shvus Yaakov ibid and Kaf Hachaim 343/35
 Shvus Yaakov ibid
 Sefer Chassidim ibid “However if he was very young when the action was committed and he does not remember , he does not need to pay”; Beis Yaakov 3; See Piskeiy Teshuvos 343/14; Lehoros Nasan 6/102
 See Pischeiy Choshen Nezikin 5 footnote 87; Piskeiy Teshuvos 343/14