Is buying a car in installments through a bank loan considered unlawful (haram) or lawful (halal), and how can expiation be made for this sin if it is unlawful?

Since you bought the car and completed the transaction, unaware of the actual method by which the transaction took place, we hope that no sin will befall you, and there is no harm in you utilizing the car. However, you must verify your future transactions and inquire before acting. And if accelerating the payment of installments leads to the waiving of usurious interests, then hasten to do so.