What is incumbent upon the one who caused an accident that led to the death of two people, one of whom is Muslim and the other non-Muslim, especially if he is unable to locate the family of the non-Muslim, and he does not possess the blood money for the deaths? Is it permissible for him to pay a sum as an endowment for mosque renovations with the intention of an ongoing charity on behalf of the deceased?

If you were negligent, you are liable for the diyah (blood money) of both individuals. This diyah is to be paid by your 'aqilah (male agnatic kin) unless they refuse, in which case it becomes your personal responsibility. You are also liable for kaffarah (expiation) for the Muslim among them, which is the freeing of a believing slave. If you cannot find one, then it is fasting for two consecutive months. What you have done by performing Hajj or other good deeds is not sufficient to absolve you of the diyah and kaffarah. You must seek out the rightful heirs to deliver their rights to them. Your presence in a country that does not apply Sharia law does not nullify these rulings for you.