Well I'm not much of a rigger, I can't help much, but your first question reminded me of when Wayne talked about how wheels get perceived when they rotate, that if they go a certain speed they seem to move backwards even and you have to hack your way through. Here in the rotation stuffs:
https://cgcookie.mavenseed.com/lessons/off-road-rotating-stuff
Your third question reminded me of a video I saw about the perception of speed in a train depending on the camera lens you used. The more narrow the field of view the slower it seemed. So maybe things will just seem different depending if you look from the viewport or your camera depending on your settings. Here's the link to the video.
https://www.youtube.com/watch?v=54Oy75Bnu_Q
It's not much of a help, but I hope it helps in some way.
Yeah the wagon wheel effect looks like it is happening in the recording.
You're animation is really coming along though. Despite the issues you are facing it is definitely coming together and the wheels turn and shocks behave well.
When the camera orbits around it can sometimes be hard to judge everything that is going on. You might try to stabilize the camera movement while troubleshooting (or just add another camera for troubleshooting purposes only).
I agree with the answers so far.
It does look like your wheel rotation is a little too fast, how many frames are you using for one loop of the track?
There was a guy some years ago, Einstein was his name, Albert Einstein, he once wrote about time dilation - the theory of relativity.
In this case, when you view the animation from the perspective of the camera, which is travelling at the same speed as the car, albeit rotating around the car, the variations in speed are less or unnoticeable, compared to a static view of the car racing around the track.
You can see the speed variation from the camera view if you focus on the background and not the truck.