Hi Mitesh,
If you're setting the exposure manually then "EC" ceases to exist. Probably what you're seeing on the meter is an indication of how the camera THINKS it will expose compared to how it thinks it SHOULD expose. So if the meter is on 02EV then it THINK it'll be under-exposed by 2 stops.
The only rule is "there are no rules". It's your photo, so you can choose how you wish to interpret the scene. THe bottom line is that the camera DOESN'T work the same way as the human eye, so what you capture with a night scene will always be different to what you see. Here's a good example; this shot was a 12 minute exposure - in reality is was so dark I had to abort an earlier shot that night when I tripped over a tripod leg, but the camera saw things just fine ...
With regards to night shooting, the camera will be incapable of capturing the complete dynamic range of the scene (the ratio of the brightest detail to the darkest detail), so something is going to have to give. If you capture the highlights correctly then other parts of the scene will be dark and/or noisy. If you capture the darker bit correctly then the highlights will be blown. In reality, it's usually the midtones you'll be wanting (a-la the middle image of your 3 above) - so my suggestion is to adjust the exposure so that these look approx correct on the camera's review screen, and then adjust them to taste in post-processing.