What is the ruling on disposing of the excess amount paid by the insurance company for repairing a damaged car if the repair cost is higher than the insurance value paid, and is comprehensive car insurance permissible if insurance is officially mandated, or should we suffice with third-party insurance?

If comprehensive insurance falls under cooperative insurance, then you are not obligated to return anything exceeding the principal amount paid, as its purpose is mutual support. However, if it falls under prohibited insurance, then you are only permitted to take an amount equal to what you paid, and you must return the surplus to the company. It is not permissible to give it away as charity if it is possible to return it to the company. The reason it is not permissible to take the surplus is that this issue resembles the matter of "al-Dhafr" (seizing one's right), where the wronged party is only permitted to take back their right without any excess.