pictures with moving subject come out fuzzy, only still or posed pictures are clear

The reason why your pictures come out fuzzy is obviously because you are trying to take pictures in lighting conditions that the camera struggles to cope with in auto mode. This is why the camera was given different manual configurations (manual M; shutter S etc)

If the lighting conditions are very low (e.g. sunrise; sunset; cloudy days or pour indoor lighting) the best setting configuration to have the camera on would be shutter or S; this will allow you to set the speed the shutter will move; thus allowing allot more or very little light into the camera; by turning the black wheel in the right top corner of the camera. The shutter speed can be set to 60 seconds (30") or a fraction of a second (2000). Basically taking the picture with a setting of anything above 200 would be safe enough to use in bad lighting conditions without distortion. Always remember that the viewfinder or LCD does not always display the correct preview of the picture you are going to take in relation to the settings you have set the camera to. And lastly it would be a good idea to put the camera down on something stable while taking the picture or to buy a tripod; this will ensure the camera to be stable while taking a picture. By using a tripod you will be able to take pictures at night without any fuzzy-ness.