What is the ruling of Islamic law regarding someone who stole from his family when he was young and now wishes to repent, but does not remember the stolen amount? Is it sufficient to donate an estimated amount to purify himself from this illicit money? And is one sinful for consuming illicit money while unaware of its unlawfulness?

What your friend stole before reaching puberty is not sinful for him, according to the Prophet, peace and blessings be upon him: "The pen is lifted from three: from the sleeper until he awakens, from the child until he matures, and from the insane until he regains his sanity." However, he must return what he stole. If he does not know the exact amount, he should err on the side of caution and give what he believes will clear his conscience. He is not required to disclose the full truth to his family; rather, it suffices to return their money through indirect means. As for someone who unknowingly consumes haram, there is no sin upon him. If the stolen money is identifiable, it must be avoided. If its status is unknown, then what is unknown is like what does not exist. The default rule for what is in a Muslim's possession is that it belongs to him if he claims so. If a man is known to have haram in his wealth, dealing with him should be avoided out of piety. As for an upright Muslim, there is no doubt in dealing with him at all.