Is it obligatory to apologize to old friends with whom problems are suspected to have occurred before puberty, or is the apology limited only to those with whom a problem is confirmed to have occurred? And does sin or a right accrue to them if they do not forgive?

A child is not held accountable for what he does before reaching puberty, with the exception of financial rights, based on the hadith: "The pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches puberty, and from the insane until he regains his sanity." Therefore, you are not held accountable for the problems you caused in childhood before puberty, and you are not obliged to apologize for them to your friends. They have no right against you concerning them. The only exception to this is financial rights, because childhood does not nullify the obligation of compensation in such matters.