You won't get very much of an effect like that with a point-and-shoot
compact digital camera; the image sensor is too small.  Simple 'auto-focus'
and 'auto-exposure' makes it something you can't easily control anyway.
But some cameras have a 'special effect' to artificially blur most of the
background in 'portrait mode' - and of course, image processing software
can do that (takes practice!).

You an only use a fast shutter speed if there is enough light.  Most
digicams let you change the sensitivity of the image detector (higher ISO
number = greater sensitivity which makes a higher shutter speed possible)
but there is a trade off in image quality with greater sensitivity.  

I doubt if you'd notice any difference in practice between point-and-shoot
cameras with maximum appertures of f/3.3 and f/2.8.  Other factors, such
as the image sensor used, the quality of the lens, and the design of the
electronics and software inside the camera, are more important.

Try looking at <http://www.steves-digicams.com/> and
<http://www.dpreview.com/> for information and reviews of particular
cameras.

Correct with larger cameras, but very small cameras have so much depth of
field you usually won't be able to reduce it much.

Image stabilization is always good to have. I wouldn't worry too much about
shutter speed in a small camera. You would seldom if ever need 1/2000 in
such a camera and might not be able to use it anyway unless the light was
very bright. Higher shutter speeds = less light passing through the lens,
and you need a certain amount of light to get a good picture.

The S510 is very flat and pocketable, if that's important to you. It has a
nice large LCD monitor but no optical viewfinder, which may or may not be
important to you. Personally I find *all* LCD screens hard to read in bright
sunlight and for that reason prefer a camera which also has an optical
viewfinder. But apparently some people don't mind the absence of a
viewfinder.

The P50, P5000 and P5100 have optical viewfinders as well as a large LCD
monitor. I like them better for that reason, and also the fact that they
have more user controls and should be more capable cameras generally. The
P50 also has better wide angle capability than the others mentioned, and
should be attractively priced. But it doesn't have real optical image
stabilization -- it has *electronic* stabilization which is not as
effective.

The P5000/P5100 are the most advanced Coolpix models available today and
priced accordingly. They both have real optical stabilization which is good.
If you're a beginner they probably have more features than you need -- you
may or may not "grow into" such a camera.

Not necessarily. In ordinary use you probably would not notice the
difference between a camera with f/3.3 and one with f/2.8, and also keep in
mind that these f-numbers only apply to the lens at the *short* end of the
zoom range -- at the long end, the f-number is invariably higher ( = smaller
relative aperture) in this type of camera, and the long end is where you'd
really prefer to have a larger aperture. Many compact/ultracompact cameras
are f/5 or so at the long end.

A longer zoom is nice dependng on circumstances, but may not be very useful
if the aperture at the long end is very small, since the longer the zoom the
more it magnifies camera shake -- so to avoid blurring the picture you will
need a higher shutter speed, and if the aperture is small there may not be
enough light for the camera to set a higher shutter speed. Generally
speaking, if you need a pocketable camera I would advise not being too
ambitious about zoom ratio. If you really want a camera with a long zoom
range I'd suggest looking into one of the several "superzoom" models on the
market -- but none of them are really pocketable. So that's the trade-off.

Neil