Re: Does this camera exist?
There isn't much that can do all that and fit into a purse.
That means not a DSLR with 28-300 zoom lens deifinitely (my first choice).
You will have to compromise on the low light, high ISO, without flash.
Compact cameras are getting much better, but they don't have sensors as big as a DSLR and so they can't gather as much light.
If you want good high ISO/low light then you want less pixels (but bigger ones) on the same size sensor. So that is another compromise you have to make between cropping, and low light.
Larger sensor is hard to find too, they're all about the same size, and most made by Sony for other manufacturers.
Continual shooting is overrated. While I use it, what I find more important is tha twhen you press the button - it takes a photo. Some compact cameras have a lag while they work out the focus, aperture, shutter speed, and then take the image. That's no good for sport capturing the moment.
Look for a small shutter lag time.
Also look at the start-up time. If your camera times out to save battery, and it takes 2 seconds to wake up again then you'll miss lots of shots. Or you'll be buying piles of batteries and turning off power saving. Either way, look for a short start-up time.
Most cameras have burst mode, even my little Panasonic LZ5 manages about 1.5frames/second for 6 frames.
What will be important is how fast it can write those images to the memory card, the shot-to-shot time for single pictures.
If that is a long time then you'll miss pictures.
I would add to that, if you don't want to change lenses, image stabilisation.
Once you use a long zoom, then you will find camera shake can ruin the photo more often.
My Minolta A1/A2 are classic examples of all these points.
A1 5Mp, A2 8Mp with the same lens, same size sensor.
A2 has more noise at high ISO.
A1 has less noise in the shadows, focuses quicker, more reliably.
Both have 7x zoom, both have sensor moving anti-shake.
A2 has 50ISO lowest speed, A1 has 100.
A2 is very noisy at 400, A1 is usable at 400.
Both have manual focus, manual exposure, and manual zoom.
Using all manual controls I can reduce shuter lag to about 0.1 second.
Too long to get good pictures consistently.
Both will shoot 3 images only, then it takes nearly a minute to write them to the card.
That means only 3 photos per LAP during a race, no good for motorsport.
Re: Does this camera exist?
Only in your dreams :D. And it will be a long time before it happens. Point and shoot cameras (that is, no lens switching) have small sensors, and small, light shutters which are by no means suitable for burst continous shooting. You might want to start looking elsewhere. And... unless your friend is very rich, I don't think she will want to buy a Canon Eos 5d to use as a point and shoot, full frame cameras as well as APS sized sensors are VERY expensive compared to the miniscule things on P&S cameras. You can always use a Nikon D40 in auto mode though. You don't even have to switch a lens. Problem is it is NOT going to fit in a purse, not even if you stuff it in there. The P&S I use, and yields very good image quality when I don't want to lug an SLR around, is the Leica D-Lux 3. Fits everything you want in there except a full-frame sensor and fast continous shooting. Plus it will fit in her purse.
Re: Does this camera exist?
But at £480 and only a 4x zoom, I think the D-Lux 3 is not right for sport.
Hockey might mean ice hockey and that's in dungeon-like lighting much of the time, with seats far away form the action if you can see over the glass.
Re: Does this camera exist?
Actually, my Panasonic will shoot 3 frames per second, up to 7 shots and at 2 frames per second, it will keep shooting until the card is full.