Must I, or those who were with me, pay for the frame that was damaged or for the extra time we played, or are we excused due to our young age at that time?

What minors commit before puberty is forgiven in terms of sin, but the rights of others are binding on them. Therefore, you must estimate the value of the extra time you used the bicycle and deliver it to its owner, and the value of the damaged tire, or what is equivalent to its repair and depreciation, because the damage occurred during a time exceeding your right or due to your breach of trust.

If the bicycle's owner is alive, this value must be delivered to him. If he has passed away, it should be given to his heirs. If you cannot identify the park owner or if they were partners, you should donate the money with the intention that it is for its rightful owner according to Islamic law.

Sheikh Salih Al-Fawzan was asked about taking money during childhood, and he replied that it is obligatory to return it to its owner if known, or to his heirs if he has passed away. If the owner is not known, it is obligatory to donate it with the intention that the reward is for its owner, along with repenting to Allah.