Well, film SLRs have always had better AF and a shutter response.  This
is because the market demanded it.  When DSLRs came along, the same
response was expected, so that's why you have it.

In all fairness, a lot of the film point and shoots are really slow to
focus/respond.  So it's more a matter of market segment than anything
else.

No: many P&S cameras have fast response now.
Yes.

Basically, because they cost more, the manufacturer can afford to
install a faster processor, and more ram along with a larger sensor.
Then there is also more room for additional specialized chips which can
do some of the work done by the CPU in other, cheaper and smaller, cameras.

You get what you pay for.

Yes, their intrinsic design makes them go faster - conventional P&S digicams
use the main sensor as their AF sensor. The circuitry analyses the image to
determine if it is sharp (in focus) or blurry (out of focus). It then
readjusts the lens to get focus.  Because there is no way of determining if
the object is blurry because it is closer than the focus point or further
away, they have to try adjusting focus in both directions until they get it
right. There is no way of telling if the image is perfectly clear - instead
what it has to do is keep adjusting the lens until it starts becoming blurry
again (overshot the focus point), then pull it back to the point where it
was at it's clearest. This system is quite slow. Because this main sensor is
a video sensor rather than a dedicated still image sensor, when the user
presses the shutter button, the sensor needs to be cleared and charged ready
to take the photo. Modern cameras can do this much faster than the cameras
of only a couple of years ago. After the photo has been taken, most compact
digi's only have one processor to take care of all the functions of the
camera, so while it is processing the image, converting it to JPG, and
saving it on the card, it can't simultaneously be analysing focus and
exposure for the next image, so you can't do anything until the camera
finishes processing the photo you just took.
A DSLR like a film SLR has a separate AF sensor that uses phase detection
techniques to determine focus. This system not only tells the camera how
accurate it is focused, but tells the camera how far and in which direction
it is out of focus. The camera can then start moving the focus motor, and
knows exactly which direction it needs to turn. While the lens is doing
this, the AF sensor continues to monitor how accurate the focus is, and can
slow down the lens motor as it is nearing focus point, so that it stops
right on focus. Because there is no trial-and-error involved, this system is
very fast.  Because the main sensor is dedicated to taking the still image
(it's not also trying to do live preview and focussing), the camera can have
it already pre-charged, so that as soon as the shutter button is pressed it
can start recording.  Once you have taken the photo, most DSLR's have
multiple processing streams, that allows them to simultaneously convert to
JPG, save the image to the card, and be analysing the data from the AF &
exposure sensors to be ready for the next photo.
If digi compacts  used some of the techniques that film compacts use, then
they would be faster. For example most film compacts use infrared or
ultrasonic autofocus systems. While not as fast and accurate as the
phase-detection system used by SLR's, these systems are faster than using
the imaging sensor. Film compacts usually also use light sensors on the body
to judge exposure, whereas most digi's use the imaging sensor for that as
well.  If a digi compact was made using an IR or ultrasonic focus system,
and with a separate light sensor on the body, and if the user wasn't using
live preview (or EVF), then then it would be possible for the sensor to be
precharged so that the camera is ready to take the photo as soon as you
press the button.  Doing this would of course add to the cost, and since it
is a very price sensitive market, that is usually only compared on
megapixels and zoom, manufacturers would be reluctant to add a feature like
this to the camera, unless it is a premium model.
Actually, my 5 year old Kodak DC3400 has these very features, and when used
with the viewfinder off it is much quicker than the more modern CX7430. The
DC3400 is only a 2MP, 2x zoom camera, and when I bought it cost more than 5
times the price of the current 4MP, 3x Zoom CX7430.