Is it permissible to take the full insurance amount or part of it, and how should it be disposed of, if a comprehensively insured car is involved in an accident that leads to its damage, and the insurance company issues a check for its approximate value with the possibility of selling it for parts?

If the insurance is commercial and forbidden, then the contract is void, and no guarantee ensues from it. Your sister is only entitled to what she paid to the insurance company, and she alone bears the damage to the car. However, if the contract cannot be annulled, then your sister may benefit from the insurance money paid to her up to the amount of the installments paid and the value of the car. Any excess should be disposed of by spending it on Muslim welfare or for the poor and needy.