Is it permissible to buy a car from a bank that purchases it then sells it in installments with interest, and is it permissible to sell it immediately upon receipt to the same dealership?

There is no objection to purchasing a car by installments and selling it to another party (Tawarruq); this is permissible according to the majority of scholars. However, selling it back to the showroom owner is not permissible if there was a prior agreement between the bank and the showroom, as this falls under usurious stratagems. It is permissible if there was no such agreement after you have taken possession of the car.