Will a girl be held accountable after puberty for taking prayer coverings from her friends and a storybook from school before puberty without her parents' knowledge, and are her parents sinful, given her current inability to return them to their owners or the school?

What was taken before puberty incurs no sin, but the lifting of sin does not mean the lifting of liability. For the hand is accountable for what it takes until it restores it. There is no sin upon the parents as long as they are unaware, and doubt about whether friends have forsaken their trusts does not negate the certainty of their ownership of them. If communication with the owners of the trust becomes impossible, then it should be given as charity on their behalf, while still ensuring its restoration should it become possible to reach them. The reward for the charity goes to the one who gives it. As for the storybook taken from the school library, it is a trust, and if it was lost due to negligence or violation of terms, then you are liable to compensate the school for its value. If you are unable to deliver it, then donate its value to the poor and needy, or to a public benefit library.