What is the correct ruling for someone who caused the death of a drunken polytheist by hitting him with his car, and is he obligated to fast as expiation for accidental killing?

The expiation for unintentional killing is the freeing of a slave. If one cannot find a slave to free, then it is fasting for two consecutive months. This expiation is obligatory if the killed person was a Muslim or a non-Muslim whose blood is protected (a Dhimmi, a person under a treaty, or a مستأمن [a person granted safe conduct]). The blood money (Diyah) and expiation are only obligatory if the error occurred due to the driver's negligence or excessive speed. Since the questioner has fasted and reconciled with the victim's family for compensation, there is nothing further required of him now.