Is the amount paid as an installment at the beginning of settling a debt that includes interest considered the interest itself, such that a new buyer of the commodity can pay the remaining installments without interest being calculated on them?

If the bank buys the car for 1000 and then sells it to the customer for 1200, the increase is a legitimate profit. However, if the bank pays the 1000 on behalf of the customer to take 1200 from him, the increase is prohibited usury (riba).

If the car's installments are usurious, it is permissible to buy it from its owner for a cash or installment price, provided that you do not replace him in dealing with the usurious bank, due to the implications of opening an account and being liable for late payment penalties.

If the seller undertakes to pay its installments, there is no harm in buying the car from him, even if it remains registered in his name, provided your right is documented. And there is no harm in the installment you pay him being equal to the installment he pays to the bank.