The most “compact” models are the Flash based camcorders. Panasonic making some of the smallest full featured camcorders and even some 3ccd models. NOTE: Keep in mind that if you want to edit the footage you shot, Flash based and Hard Drive based camcorder files may need converting before you can edit them.

I use a Sony a200 as my daily carry around camera. I goes everywhere with me and I shot something everyday with it. I have shot sporting events with it and a faster “Burst” mode would helpful. The a200 is an entry level D-SLR so the frames per second speed is not as high as a pro range camera. You may want to look at the a350 which is a 14.1megapixel (compared to the a200 @ 10.2 megapixel) and a little faster Burst speed frame rate(almost 3fps). The a700 would be better due the the fact that it is more on the Pro level and has the faster frame rate(5fps).
Getting the 75-300mm is really a good idea for sports photography. It will make getting the tight shots from the side lines MUCH easier.
And the image stabilization built into the camera body is a big plus.

Not sure I understand your question. If you want to transfer the “data” most cameras use USB cables. The connection on the camera may vary from brand to brand and model to model, check the connection with the camera before you purchase. If you are speaking of the “Date”, that information is embedded in the photo information and is transferred with the data along with shutter information, ISO, amount of zoom used,..ect. This information can be viewed in most photo and image programs under image info or file info.

Unless there is a corruption or bad areas in the memory all photos should download. When you have taken photos and transferred all of them always Re-Format the memory not just Delete pictures. Formating will insure that the images a kept in one continuous file.
Some cameras also allow you to “Lock” photos as an erasure prevention safety. This may be found in the menu area.