Is working for a company that facilitates a customer's purchase of products by paying the full price to the original producer and allowing the customer to pay in installments without any increase, and imposes a fixed, symbolic late payment penalty for delayed payment that goes entirely to charities without entering the company's accounts, permissible or impermissible?

So long as the company's work revolves around paying the price of the product and collecting it without any increase, then there is no harm in taking up that job. As for the issue of imposing a fine on those who delay payment, to be donated to charitable causes, this is a matter of disagreement among scholars, and most of them prohibit it. However, this does not prevent you from working for the company. The company's management should be advised to avoid that condition.