Is the company's activity, which involves selling cars to customers in installments, with the cars remaining in the showroom's warehouses and the customer selling them directly to the same showroom without seeing them, Islamically permissible? And what is the ruling on working in this company as a cashier? And are the salaries received from it lawful?

Nothing appears to prevent the company's activity. Installment sales and the sale of a car with a customs card, which removes ambiguity, are permissible and valid. Possession is achieved by vacating, and it is not necessary to move the car from the showroom. It is also not prohibited for the company to buy the car from the showroom after selling it to the customer, unless there is an agreement or collusion that makes the showroom an intermediary in the sale of the specific item. Therefore, the brother's work in this company is permissible.