Is it permissible for an employee to request a car from his institution, knowing that it has comprehensive insurance, and is it permissible for him to accept it if it is given to him without his request, knowing that it has comprehensive insurance?

It is permissible for an employee to request or accept a car from their employer, which benefits from comprehensive insurance. The sin of prohibited commercial insurance falls upon the person responsible for it. As for cooperative takaful insurance, there is no harm in it.