My answer to 1 is a guess, my answer to 2 & 3 are not.
1) This is a difficult question. I believe that most paparazzi own their own equipment. They are free-lancers. This means that they can't always afford the expensive cameras, but they can't have the cheap ones (because of what they do.) So while they might want the highest resolution cameras (a Canon 1Ds or the latest 1Ds MkII) they are 8K, and cost a lot to issure. My guess is that they would instead go with a Canon 1D or 1D MkII. That gives them very fast shutter speed, fast buffer writing and great AF performance.
2) An SLR (stands for Single Lens Reflex) camera is a camera where when you look through the view finder you look though the lens. You are seeing what the camera sees. Most (but not all) have replaceable lenses, which makes them more flexable. Your wrong about how an SLR works. There is a mirror but it isn't used to capture the image, it redirections the view from the view finder through the lens. When you take a picture the mirror moves out of the way so the light strikes the film (or sensor.)
There are several advantages of using a camera of this type
- You see what the camera sees, so its much easier to frame the shot.
- With a depth-of-field preview button you can see how large the DOF is and tell where its placed. This lets you know how much (and what) will be in focus and what won't be.
- most (90%?) of all SLRs have replaceable lenses. This makes them much more flexable, and it lets you spend more money and get better lenses or spend less and get cheaper lenses. This is good because most lenses on fixed lens cameras are a compremise between cost and quality. If you care about really high quality this lets you get it.
- This isn't inherent to SLRs, but right now the quality of the parts are better (they cost more, so they can be.) This means you get faster AF, better metering, better less noise at higher ISO values. If camera makes wanted to they could do this in the lower end point-and-shoot consumer cameras... but they don't because they want those models to be cheap.
3) There are several issues with this one that are related. To stop action you either need a high shutter speed (which just stops the action) or be really good at panning with the motion you are trying to capture. If you are good this will produce an effect where the background will be blured but the subject should be sharper. This last one is what is often done with race cars.
To get a fast enough shutter speed to stop a speeding car is very hard. I truly don't know how fast it would have to be.