I don't have the lens, and plus I'm a Nikon guy, but I can answer your questions anyway.
First, regarding the focus. Assuming the available light is adequate, the lens should focus fine. That said, if you're zoomed in all the way at 5.6 even in ideal conditions you may find yourself limited by the slower lens. I would advise against the kit super zoom and instead recommend bringing a short lens and a long lens.
Second, regarding the sharp car blurry background pic - there's two things happening there.
First, as you suspected there's a slower shutter speed enabling that blurred look.
Second, the photographer was doing a panning track of the car as the shot was being taken, so as to keep the car sharp but let the background blur out a bit to imply movement.
YOU WILL WANT TO PRACTICE THIS A LOT BEFORE RACE DAY!!
Here's a pic I took that replicates the look I think you're going for (I've never been to one of those fancy races, though)
DSC_7090 by
Zack, on Flickr
It was shot at 70mm on a 70-200 2.8. Aperture was f/16. Shutter speed was 1/60. ISO 100. Make sure the lens you use has VR/IS and you know how to make the best use of it.
Your shutter speed will likely be able to be a fair bit higher considering the higher speed of the car. Thus your aperture will be able to be more open.
There's no real "here, use these settings, they'll work" because nobody knows the conditions that day. But maybe it'll give you an idea of what goes into a shot like that.