What is the ruling of Islamic law on the Murabaha transaction for purchasing a car in installments, and is the promise to purchase legally binding, such that the bank is entitled to compensation if the client reneges on their promise?

The transaction mentioned is valid, and the questioner's concern regarding the promise and the necessity of fulfilling it does not invalidate its permissibility. A promise is religiously binding unless there is a valid excuse, and the effect of this obligation is either to fulfill the promise or to compensate for the harm caused by its unfulfillment without a valid excuse.