How can the rights of people be compensated from whom my mother took things without their knowledge, and would charity or helping the poor suffice for that?

What your mother took before puberty incurs no sin upon her, but she must guarantee its return to those from whom she took it. As for what she took after puberty, she is sinful for it and must guarantee its return, based on the Prophet's (peace be upon him) saying: "The hand is responsible for what it took until it returns it."

It is obligatory to return established rights to their owners if possible, even through indirect means. If the owner has died, their right should be given to their heirs. If it is not possible to deliver the right to its owner, then it should be given as charity on their behalf to the poor and needy. If she does this, her conscience will be cleared of those rights. She must also repent for what she took after puberty by feeling remorse and seeking forgiveness.