Is it permissible, in Sharia, to purchase a car by installment from a financing company, given that the company is owned by the same person who owns the importing company that buys its cars with bank loans?

The fact that the company borrows with usury does not affect the transaction between you and them, as long as the transaction itself is permissible according to Islamic law. This is because the prohibition of usurious loans relates to the liability of the borrower, not to the specific item purchased with the loan. Furthermore, the company's capital is mixed, and transactions with mixed capital are permissible.