This type of shooting is referred to as “Burst Mode” where the camera takes several photos in a row. The icon for this mode looks like several squares laid overlapping each other. It will either be a button or found as a setting in the menu area. Almost ALL cameras have this feature now. Higher end Pro type cameras are best at burst mode and shot 6 or more Frames Per Second and will keep shooting as long as the shutter button is pressed. Compact, Advanced and Entry level Digital-SLR cameras will be at a much lower speed with 3 FPS being the best.

A Digital-SLR would be best for you. One that is 14 megapixel or higher. This will allow you to pick up more detail and be able to crop with still retaining lots of data. You will need a faster, more light sensitive lens to shoot in dark areas.... f/2.8 or preferably f/1.8. Image stabilization either on the lens or body of the camera would be highly recommended. Canon, Nikon and Sony would all have a camera that will work for you situation.

All batteries have a little internal resistance and will loose their charge over time. There is no exact length of time it takes for the battery to discharge. Factors such as quality and size of the battery, age, how many recharges the battery has had, even humidity conditions and temperature could also effect the hold time. On average a good battery should hold a charge out of the camera for up to a month or two, perhaps slightly more. In camera (not being used) that time might be greatly reduced to one or two weeks.

There are Many Digital-SLR cameras to choose from, each with unique benefits from each manufacturer. Be it more lens options, in camera stabilization, wireless flash control, live-view....option lists keep getting longer and longer. Popular opinion is that Canon, Nikon and Sony have the top slots. Where I can't suggest one manufacture over another I will suggest some things to keep in mind while choosing a camera:
1)Physical size of the camera. Canon Rebel, Nikon D40 and Sony a300 models are a good starting point as the bodies of the cameras are more likely to fit better in smaller hands. Professional range cameras a much bigger, bulkier and heavy for a reason. Take her to the nearest BestBuy and get the cameras in HER hands and find the one that feels good to Her.
2)Lenses...very important. The two most common lenses are the stock lens supplied with the camera and a Zoom Lens...usually up to 300mm. Image Stabilization is really a nice feature to have, and is nice to have in the Lens. Some camera bodies have built in stabilization.
3)A good Tri-pod. Stabilization on the camera or lens is great only to a certain point. A GOOD tri-pod is a must.
4)Extra Batteries and Memory Cards. You can NEVER have TOO MANY.
5)Have her take pictures of EVERY THING. That way she will find her favorite subjects and what she's best at shooting.