Am I obliged to pay the blood money for a dog I hit with my car, given that I do not know whether it died? And if I wanted to pay it as a precautionary measure, how much would it be and how should it be paid?

The questioner bears no blame or sin for what happened to the dog, even if it died because of him. Scholars differ regarding one who kills a owned dog: some oblige its value, while the majority of scholars do not require compensation. It is most probable that the dog found on the highway had no owner, and the questioner was unable to avoid it.