Yeesh, and now some help that applies to P&S cameras...
(1) You can't really adjust focal length that much. The best you can do is use the optical zoom as much as possible, and shoot from there. The reason to do this is because it minimizes the apparent distortion of proportions of the face caused when you use a wide angle and
(2) Your ISO should not be set to 400 all the time as your sig suggests. You should be able to easily use ISO 100 in daylight conditions. (The first shot was at 1/500; given that, you really should be able to get away with two stops less light by going down to ISO 100.)
(3) It's called "noise". "Grain" applies to film, and "noise" is a different beast altogether. Compact CCD sensors in P&S cameras have some of the worst signal-to-noise ratios, so you really need to be aware of this and turn down your ISO.
(4) The first shot is actually pretty good. Reproduce whatever you did for it (but turn down ISO to get it even cleaner). It's the cleanest of the lot, and the colours seem to have been reproduced faithfully.
(5) Never, ever, ever use the digital zoom on the camera. Ever. All it does is blow-up (using terrible algorithms) a smaller part of the sensor. This drastically increases noise. You can do better by cropping, removing noise, and then upsampling the image on your computer.
If you aren't using some sort of post-processing to remove noise, you should be. There are some fantastic programs out there to remove noise. If you have Photoshop, I'd recommend either Topaz DeNoise or Nik Software Dfine. Either work fairly well, though personally I'm leaning toward DeNoise. I'd like to post an example of the second image with noise reduction through DeNoise; it would easily produce a presentable image (though with that level of noise it's liable to become very soft; much of the detail has already been lost).
Lastly, you might want to consider a camera that performs better. A decent P&S can be had for $100, and if you spring more money on it you could get one that performs quite close to a lower-end DSLR. Quite a few P&S cameras even have CMOS sensors now, which is a plus.