I think I need to zoom out a bit to explain. We talk about "oil" but what we're really talking about is just hydrocarbons. Take a look at this diagram:

The only difference in the many forms is how the hydrogen and carbon chains are ordered. Add or subtract a few and it becomes a different substance with a different name. We can technically make hydrocarbons from atmospheric air. This includes methane and even gasoline can be made from the air surrounding us. We don't do this because its expensive and pulling petroleum from the ground has most of the work done for us.

So to answer your first question: Most of the hydrogen and carbon in the synthetic oil in your car today probably came from petroleum, but that petroleum was broken down into raw carbon and hydrogen, then the oil molecules were built into motor oil.

Petroleum became too expensive, we'd use different sources besides petroleum for carbon and hydrogen input needs.