Am I entitled to keep the 15,0 Riyals that the bank will deduct upon early settlement of the car loan, for the car I bought in my name for my friend, after I have paid the full amount, without informing him of that?

You bought the car for your friend, and the money you paid from your own funds does not make you the owner of the car. You have the right to reclaim what you paid. Whatever amount the bank discounts from the price is a discount for your friend (the principal), and you are not allowed to demand it from him with an increase, because that is considered a loan in which an increase is not permissible.