What is the ruling of Islamic law regarding a girl who killed another when she was seven years old, without the knowledge of her family or the family of the victim about the crime, and what is her expiation, given the impossibility of paying the blood money or knowing the victim's family, and that both parties are non-Muslims, and that the incident occurred in a non-Muslim country?

What your friend did—killing at the age of seven or eight—is considered accidental killing (qatl khata'), which necessitates the payment of blood money (diyah) by her 'aqilah (male relatives responsible for paying blood money). This blood money would be half the diyah of a Muslim woman, because the slain person is not Muslim. She is also required to perform the expiation for killing, which is fasting for two consecutive months.