What is the ruling on comprehensive car insurance, and is it permissible to take partial compensation from the insurance company of the party responsible for a collision, and what is the ruling on not having comprehensive car insurance in order to receive compensation for all damages?

Cooperative Takaful insurance is permissible, and it is permissible to subscribe to it and to be insured by it against all risks. If the person who hit you was at fault, there is no blame upon you for taking what the insurance company paid as compensation for the damage you sustained. If the amount paid is less than what you deserve, then the car owner must pay you the remainder if his insurance company does not pay it.