Why videos taken in the dark has color artefacts (noise)?
The noise in dim-lit environments is a result of how digital cameras work. The exposure of a picture or video depends on three essential parameters: lens aperture, shutter speed and ISO. The first two are about how much light falls on the camera sensor. The larger the aperture, the more light can enter the camera. The slower the shutter speed (i.e. the longer the exposure), the more light can enter the camera. ISO/gain is a digital amplification of the digitalised sensor signal By amplifying the signal, the camera can essentially make it brighter. However, the noise that is captured is also amplified. 

What's important to understand is that if you were to expose a light and a dark scene using the same aperture, shutter speed and ISO, the dark one wouldn't have more noise than the light one, it would just be darker. The noise is a result of the camera increasing the ISO/gain to achieve a well-exposed scene (which for the camera means a normally distributed histogram).


  1) Why that noise is added at all? why cant the image could be static, i mean, where is black color, there should be black without noise... (same for other colors...) why colors are not static and why this annoying noise is added? 


What probably happened with your example video is that the camera noticed a dim-light environment and cranked up the ISO/gain to achieve a well-exposed video. This inadvertently increases the noise of the video as well. What you can do to circumvent this is to switch to a manual exposure mode where you set the aperture, shutter speed and ISO manually. This way, you can set your camera to underexpose the image. It will turn out rather dark, but less noisy. Keep in mind though that this does not mean you should just underexpose your video and just turn up the brightness in post-editing. This will once again increase the visible noise, because it's basically the same thing as increasing the ISO, only less efficient. So there's a tradeoff between noise and exposure as well. 


  2) is there any method in photocameras (mobile, CANON etc..) , to force camera to record without noise (like professional videocameras do)?


High-quality lenses will usually be faster, meaning their minimum f-number (maximum aperture) will be lower. A larger aperture means more light entering the camera in the same amount of time, so with a larger aperture you will get a brighter image than with a smaller one (while shutter speed and ISO stay the same).

High-quality cameras will usually have slightly better low-light performance, meaning there will be less noise under the same circumstances with the same settings, but that difference is rather negligible in scenes as dark as the one in your video. 

You can also use a tripod to steady your camera, allowing for slower shutter speed (meaning each individual frame of your video will be exposed for a longer time). However, the shutter speed can't be slower than the inverse of the framerate for obvious reasons, so that will only do so much to brighten up your scene. 

What you really need to do to lower the noise is bring in more light. You can still darken the video in post-editing, but if you are able to shoot a well-exposed video with a low-ish ISO value (the meaning of low in this context depends on your camera model), the resultant video won't have much noise regardless of how you decide to edit it. Alternatively, if you want an underexposed video (if that is the style you're going for), you can just set your camera to manual and purposefully underexpose the scene as described above.