What is the ruling on buying a car from a bank that describes its transactions as Islamic, according to the steps mentioned, and is this transaction free of prohibitions or doubts?

If the bank purchases the car, and it enters into its ownership and guarantee, then sells it to the ordering party with a separate contract and fixed installments, there is no objection to that. The bank’s condition of mortgaging the car with it as security for the price does not affect the validity of the contract, according to the preponderant opinion. If the bank disposes of the car by selling it upon default of payment and takes what remains of the price due to it, returning the remainder to the customer, there is no harm in that, provided it is based on a prior agreement, unless the customer retracts the authorization.