I´m afraid your images are out of focus. Both, the sunset and the star shot. Does that happen with your daylight shots too? If yes, you need to go to Sony service. If no, better use manual focus for star shots. Usually that works pretty well, if you use the loupe function of your monitor. If it doesn´t work for you for whatever reason, focus on something that is bright enough to help you focus and is at least 5m away, 10m to be on the safe side. On a wideangle lens like the one you are using, everything beyond a certain distance is infinity focus - so the stars are well focussed if you focus on an obect that is in a distance of 10m.
I checked your image data on the star shot
16mm (equal to 24mm full frame)
30sec (is just about right, google "500 rule for astrophotography")
f4 (lower is better for astrophotography, but this is as good as it gets for your lens - don´t think about buying a new one yet though, get the best out of the equipment you have before upgrading)
ISO400 (You have to ramp up ISO quite a bit to see more than the brightest stars on your image, even when it is well focussed ISO 1.600 or 3.200 should give you better results).
One more thing to consider when photographing stars is light pollution. If there is too much light at night in your area, blacks won´t be black enough to give your stars the contrast that is needed for great pictures. There is great website that gives you an idea of how much light pollution is in your area and helps you find great spots:
Light Pollution Atlas 2006