What is the ruling of Islamic law regarding the blood money (diyyat) currently in practice, which is customarily estimated at thirteen thousand Libyan dinars, of which three thousand are for condolences and ten thousand are paid after reconciliation?

The blood money (Diyah) is Islamically stipulated for both Muslims and non-Muslims. The amount mentioned in the question is far less than the full, Islamically mandated blood money. If the victim's guardians are not satisfied with it and demand the full blood money, they have the right to do so. It is not permissible to rely on custom or law that contradicts Islamic law.