just look up to the sky at night. They are so dim that you cannot really distinguish their hue.

Hard to tell without being closer :) Nebulae might not even emit that strongly in the spectrum that we humans can see. A lot of these pictures are taken with special narrowband filters that isolate wavelengths for specific components, such as Oxygen or Hydrogen. Then these narrowband images are combined and assigned to the R, G, B channels. A popular palette is the "Hubble Palette" because, well, that is what the Hubble uses.

Depends on the filter used. I am assuming the author is using one of these hydrogens (probably Hα) and O-III and S-II. Each of these black-and-white images with this filter are used as the data for a single RGB channel in an image. Their wavelengths are, and would like like to the naked eye [1]:

Hα (656 nm) bright red

Hβ (486 nm) deep blue

O-III (496 nm and 501 nm) greenish blue to green

S-II (672 nm) deeper red

The color mapping the author uses is called the Hubble Space Telescope pallet, where hydrogen = green, sulfur = red, and oxygen = blue.

[1] http://pages.cs.wisc.edu/~yetkin/code/wavelength_to_rgb/wave...

Depends on what you mean by real colors. The light is so faint, that human eyes cannot make it out. However, long exposure photography with a CMOS sensor will bring out colors without any filters. Are those the real colors? There are tons of examples of these types of shots. Search for The World At Night (TWAN) for some great examples

To the naked eye from earth, it looks black and white, and you wouldn't be able to see that much detail. What they "really" are is more complicated, as indicated by other responses.