Definitely sensor dust, not lens dust, on Droider's and Bartman's images. Any camera with a removable lens will be prone to this issue. Some cameras come with an ultrasonic self-cleaning capability but in my experience it's only marginally effective. Here's the rules:
- Remove the lens as few times as possible
- ALWAYS turn the power off before removing the lens - otherwise the electrostatic charge on the sensor will attract dust like a magnet
- Once the lens is removed, keep the open throat of the camera pointed downwards
- If not refitting a lens immediately, put a bodycap on the camera
- If operating in a really dusty environment, put the camera inside a sandwich bag and tape around the lens barrel
For cleaning, always try a blower first - but NEVER use "canned air" (it can blow liquid chemicals onto the sensor surface). VisibleDust (among others) makes an illuminated magnifier that will enable you to examine the sensor surface. The Arctic Butterfly brush is also very useful. Be careful, however, of the expensive swabs and liquids sold for sensor cleaning: they can create more problems than they solve. Personally I use a high quality chamois leather cloth (designed for camera lenses and spectacles) wrapped around a small, square-ended wooden spatula (like an ice-lolly stick). Remember, you're not actually touching the sensor but a piece of glass in front of it so it's not as delicate as you might think.
Sensor dust will show more when you shoot with a smaller aperture. Dust that may not show up at all at f2.8 will be horribly visible at f/22.
Regarding resizing images, whenever you reduce an image in size you will need to sharpen it to restore the crispness. The greater the reduction, the greater the need to sharpen it subsequently. Every image editing program should have a sharpen command of some kind. The best tool is the confusingly-named "unsharp masking", which allows fine control over how much sharpening is applied. Judge it by eye: move the sliders until it "looks right".
Lightroom gets a lot of press, but I prefer
DxO Optics Pro - a less-known but superbly powerful raw processor that has a too many advantages to list here.