<1>
f/8.0 is often the "sweet spot" for lenses on 35mm SLRs however on a small
sensor camera like a Canon PowerShot that aperture is probably causing
diffraction - there's a good reason the aperture doesn't go any smaller than
that!
Light spreads out when passing through a small opening like the aperture on a
camera and this results in loss of sharpness. The smaller the hole the more
spreading you get, so there comes a point where stopping down a lens results in
lower peak* sharpness. Due to compact lenses having (and requiring) shorter
focal lengths, f/8 on a compact will result in a smaller opening than f/8 on an
SLR, therefore you will get more diffraction.
*I said peak sharpness, as average sharpness can increase after the point where diffraction sets in due to increases in depth of field. However if you don't need the depth of field, try shooting at f/4 instead.
So GH2 - 300mm/f5.6 or 100mm/f4 gives the sharpest pictures. f4 gives narrower depth of filed so its average sharpness is lower than f5.6.
<2>
focal length - aperture - ISO - shutter speed - IS - Flash
The highest peak sharpness: not long focal length + low f value (wide
open) + low ISO + fast shutter. So, if handheld, 100mm + f4 + ISO 160
+ faster than 1/200 + Image Stabilization (IS) On = highest peak sharpness
in theory. My understanding is that aperture & ISO are the major
factors. Shutter speed has to be fast enough to freeze the shoot.
Once reaching the threshold, faster shutter will not make too much
difference. Long focal length blurs the pictures because of camera
shaking. So IS can help if shutter speed cannot be increased. Flash
also helps in low light and shooting fast moving objects. In
conclusion I should wide open my lens unless (1) need more depth of field;
(2) limitation of lens - lens doing bad when it is wide open.
<3> Sharpness is a result of eliminating various problems:
You can avoid motion blur by ensuring you use a tripod, set your camera to use mirror lock-up (if available) and using a remote trigger or timer. You also need to ensure your subject is still! Alternatively, use a flash to isolate any movement to a single instant.
You can avoid focus blur by using autofocus or by manually focusing. My camera allows me to zoom the image on the back screen of the camera to get really precise manual focus. You can also increase the depth of field to ensure more of the image is in focus.
You can avoid lens issues by using the sweet spot of your lens. This is generally in the middle of the aperture range, but you can test by taking a range of photos, one at each aperture setting provided by your camera, and then choosing the one that looks best. See this answer for more information and an example.
You can avoid camera issues by checking you are using the maximum available quality of image, by turning off noise reduction, and by checking any other settings that could affect sharpness.
Some lenses are sharper than others but you should be able to achieve good results if you use this technique.
<4>