Is the car still the responsibility of the questioner or his friend, after the seller repossessed it due to non-payment of installments, knowing that the friend did not transfer its ownership to his name as he claimed?

If the car is purchased through a lease-to-own system, and the contract is one of the permissible forms Islamically, then it is not permissible to terminate it except with the consent of the leasing company. The company has the right to lease the car to whomever it wishes. However, if the contract is one of the prohibited forms, then it must be terminated, and the fair market rent must be paid to the company.