Is it possible to install Unix OS on computer with NT OS? I understood that Linus is kernel used when computer reboot. Do they work together in computer system?

Yes, linux can coexist on a machine with NT.

Why do we need Linux or Unix, when there are other operating systems like Microsoft OS and Mac OS?

And why do we need Microsoft or Mac when there is Linux and Unix?

I do not think that anyone can answer that one in a universally valid way. Each operating system has its own advantages and disadvantages. One good reason to prefer Linux is to cut costs, another is having total control over your computer or network. MS and Mac are proprietary products, i.e. the user has only rights to the extent that the manufacterer is willing to grant any. Also, you do not get to see their inner workings (top secret). Not to mention that it is absolutely illegal to modify anything. Just think of the whole DRM issue with Vista. What gives MS the right to decide for its users which media can be played and which not? Linux on the other hand favours total freedom: if you want to, you can access all the code, modify it, make your modifications available to others, etc.
Linux does not place restrictions on its users because it believes that people are mature enough to be responsible for their own actions. If some use illegally obtained media, for example, that is their business and not a reason to place restrictions on the rest of the community.

But why not try it? Linux comes at the absoslutely amazing price of $0 (unless you choose a commercial version instead of a free one but there really aren't any crucial differences between those, however, unless you are running a (major) business).

Perhaps you should tell us what your REAL question is..... Pending that, I offer an old truism:
If you don't know why (or if) you need something, then you probably don't need it.

To answer your original question: The first thing I would do with a computer with NT is get rid of NT--If you must have Windows at least get 2K.

Here's my big question:

What do you want the computer to do? What you want to do determines what tools you need.

Using the wrong OS for your job is like using a hammer to install a car window.

No more replies to this unless OP re-appears--we have already requested clarification of the question.

(I think this maybe should be a informal rule)

Why would you need cake when you can have bread?