What should I do with torn copies of the Qur’an that are of no use to anyone, and am I sinful for their damage, and what is its expiation, if any?

A discerning child is permitted to touch the Mushaf (copy of the Qur'an) for the purpose of learning, and he must be urged to respect the Mushaf. It is preferable for him to be in a state of purity (tahara). If the child cannot carry a large Mushaf or protect it from damage, he should be given a small Mushaf. If his learning requires a large Mushaf, then he is allowed to have it, as the benefit of learning is greater. If copies of the Qur'an are damaged, those that are still usable should be given to someone who can benefit from them, or placed in a mosque or library. As for those that are damaged, they should be disposed of by burning or burying them in a respectful place. Atonement for their loss is achieved through repentance and good deeds.