When did movies first start to show real world from inside a car and not a studio-based rear projection? What was the first movie that contains car sequences all made with real action shots?
I think, it is more difficult to put a camera in a automobile or on a truck then on a vehicle on rails.
I found some examples of early shots, but I'm not sure if they fit your criteria of inside a car. The shots I found are from a car, not inside.
I found some very early snipplet with a scene from a rail bases car:
Algier 1896: http://www.dailymotion.com/video/x11mo5_alger-1896-video-rare_shortfilms?start=77 The camera starts its movement at approx 1:20
It is considered to be the first example of a phantom ride and features a train travelling along the West Shore Railroad in Rockland County, New York and then through the eponymous tunnel.1
I haven't see the film, so I'm don't know the scene.
Another early moving shots I found was from a boat: Panorama du Grand Canal vu d'un Bateau (1896)
Rear projection techniques came after filming in "the real world", as the filming of rear projection requires that the camera and projector be synchronised to avoid shutter flash. This technology did not exist in the silent era, so any motor vehicle filming would have been done live.
Its probably worth noting, though, that the filming was usually done with the car either on a flatbed truck, or being towed by a camera truck.