Something that I have found helpful in GT4 is to set the MANUAL focus on the CENTER of the car. The game is VEREY picky on how it focuses and you will have to play around a LOT in order to get the perfect shot.
If you focus in on one section and another part of the car is blurry, move your focal point a LITTLE bit. Then just keep moving it till you get the desired picture.
It can take a LONG time to get a good shot, and sometimes, with certain camera angles, you will NEVER get a nice one.
I would also never use an aperture larger (smaller number) then 5.6 - 8 for the shots you have posted thus far. Any wider and you will have focus issues out the butt ...
Also, in order to get a better "stop" in the motion of your car, use a camera angle that is not right on the car. Something that you have to zoom in to over 180mm in order to get proper composition.
In GT4 the closer you are to the car, the faster shutter speed you have to use and the LESS blurry your BG will be. It is because of how the camera is tracking the car.
Just think: if YOU were holding the camera, and a car rushes by at 30 feet away, you will be turning pretty fast to keep up with the speed of the car. Now if it were 100 or more feet away, and you were zoomed in, you would not have to move as much or as quickly on order to track the motion and could therefore use a slower shutter speed.
I hope that that helps ...
Good luck and keep at it! 👍