What is the Shariah ruling on my fiancé completing the payment of a usurious car loan, which is considered his source of livelihood, and is the money earned from the car's operation considered lawful or unlawful, and what is the fate of the car if the loan is paid off with lawful money?

The car belongs to your fiancé, whether the bank bought it and then sold it to him, or he borrowed its price with usurious interest. The sin of usury falls on the borrower, not on the car, and using the car and what results from it is not forbidden. There is no objection to the money he will use for marriage or spending being earned from his work with this car. You are not required to hasten the repayment of the debt to the bank, unless the bank will exempt you from the usurious interest.