What is the ruling on sharing a car with a friend such that the resulting amount is divided equally into three parts (for me, for the driver, and for car maintenance and fuel), and what is the ruling on a sheep owner partnering with a shepherd such that each of them takes half of the money from selling the sheep?

The two scenarios mentioned are a subject of dispute among scholars. As for giving sheep to someone else to take care of them in exchange for half their price upon sale, this involves jahalah (ambiguity) and gharar (uncertainty/risk). The correct alternative is for the caretaker to tend to them for a known period in exchange for a portion of the sheep themselves, with the increase (offspring/growth) being owned jointly by both of them.