In portrait mode. Focus the subject, then move towards the subject half pressing the shutter button (by reducing camera-subject distance and increasing subject-background distance.

No.

I presume that it is your shutter speed is probably to slow, for the camera to be used handheld. The camera slows the shutter speed to allow enough light in to get the image, because it is dark there is less light, so the camera has to expose for longer. If you are shooting hand held, you will constantly be moving and there for the image will blur. There are ways that you can try and improve the photo. Change the ISO, use flash (though this isn't always the best option), change the way you hold and support the camera (surprisingly this does make a difference), use a tripod, etc.

This is one of Nikons cheapest cameras, I don't think you will get anything close to this price.

14.1mp. I wouldn't worry about the megapixel count on pretty much any modern camera. You can print out good quality A4 photos with just 4mp. Look more for the features and ISO quality.

I would suggest, that you have too slow a shutter speed. You camera is probably compensating for the lack of light and is slowing down the shutter speed. Another factor is how much you are zooming, the longer the focal length the faster you have to have the shutter speed. I would suggest, you put the ISO up higher when shooting at night. use a tripod, monopod or have something to support or rest the camera on. Hold the camera better, don't stick your arms out when taking a photo. Try different modes like night mode etc. Flash, this sounds the most obvious but generally with on board flashes the lighting is generally quite harsh, so be careful, You can help by putting a white piece of paper, tracing paper or baking paper front of the flash, that should defuse the light slightly. Shoot, with a much light as you can.