My question has to do with the selling of cars to the public. If a customer cannnot afford the car outright and would like for me to offer in-house financing for the vehicle, is it permissible to add a financing fee since I will be taking on the risk?

If you are going to finance him, i.e, giving him cash to buy a car, then you can not ask him to pay you more. While if you are going to sell him a car, that worth's 1000 $ cash, with 1100$ on 3 months, then it is OK.