Is 'color' characteristics of a body or characteristics of light? 
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*In situation when body exposed by light, is 'color' characteristics of a body or characteristics of light? Is there any difference on macro/micro levels?

*Will exist such term as 'color' in parallel universe where electro-magnetic waves doesn't exists?
 A: The "color" of a body is not a property of the body nor of the light it reflects or emits, but rather of the human eye and brain that receive and process the light. Of course, this is based on a property of the light, for this is how the eye receives the information that there is some object in there in the first place. 
This property is the spectrum of the light: the relative intensity that the light has at different wavelengths. It is easily observable by using a prism or diffraction grating to spatially separate the components with different wavelengths.
Within the human eye, the spectrum of the light gets translated into nerve impulse signals which are later interpreted by the brain. This translation stage is lossy: the nerve signals contain less information than the spectrum did, and it is not possible to reconstruct the latter from the former. To put this another way, there exist light sources (of, for example, 'yellow' light) which have different spectra but nevertheless look the same to human eyes.
To a good approximation, the nerve signals can be considered to consist of three 'channels': one for red, one for green, and one for blue light, which correspond to the spectral regions where three types of retinal cells are most sensitive. The combination of how much of each of those signals you receive then gets interpreted as your subjective experience of color. 
Other animals also follow similar models, but the number of channels can vary between species. Some have only two types of receptors, and some have more than three, ranging from four or five to sixteen, in the case of the mantis shrimp; some animals like certain snakes can see in the infrared. In as much as it makes sense to ask about the subjective experience of an animal, there is really no way for humans to comprehend what vision with more than three channels 'feels' like. Certain humans do have one or two of those channels impaired, and are known as colorblind; to a certain extent it is possible for non-colorblind humans to understand what colorblindness is like.
And as for your second question, it would depend entirely on the sort of beings that inhabited the hypothetical world, whether their cognitive structures and subjectjve experiences were analogous to ours, and whether there was some other physical property which they detected through analogous mechanisms. In short, the question doesn't make much sense, really.
A: Colours are just a result of our brain and eyes measuring and processing the light that we see. In fact, I wouldn't be surprised if animals with the capability to see infra-red see different shades of temperature as different colours. Or for example a bat - maybe they see surfaces with different (sound) reflective properties as 'colours'.
Colour in the physicist sense really only refers to light with a specific wavelength.
A: Color is nothing but interpretation of electromagnetic waves into various
nerve signals by our brain. It is the property of the object to
reflect various wavelengths when photons strike their electrons. Electrons 
then vibrates up and down atleast 1000 times each second emmiting
electromagnetic waves which our eyes receives. Each different wavelength
of visible spectrum has its own color representation by our brain.
A: Besides the physiological part of optic nerve and brain, we call an object coloured if it reflects light of a specific wavelength (or wavelengths) from the complete visible spectrum. And we call light coloured if the light source only emits a part of the complete spectrum. 
