Is it permissible to accept a car provided by the company under the mentioned conditions, and would I incur sin if the details of the contract between the company and the bank involve usury, knowing that the company provides public transportation and it is not possible to take a transportation allowance or the installment money if I refuse?

It is permissible for the questioner to take the car, especially since he does not know the true nature of the contract between the company and the bank. Even if the contract is assumed to be corrupt, what is received through a corrupt contract becomes owned, and the car, after its purchase, becomes the property of the company. The sin pertains to the company's responsibility, not the questioner's. A person is only burdened with their own actions and is not questioned about the actions of others. For "whoever earns a sin, he earns it only against himself," and "You who have believed, take care of yourselves. No harm will come to you from those who have gone astray if you have been guided," and "You are only responsible for yourself."