Stability of the amplifier

I know that characteristic that explains stability is K coefficient and it's must be more than unity. But can you explain me basically, how one coefficient may describe behavior whole circuit? What thing does this coefficient describes? Stability it is too generally. More precisely.

K-factor does not tell you "all about stability" of a circuit but just a simple prediction.
As you know well, stability term is coming from classical circuit theory e.g.Poles, Zeros, Bode Diagram etc..
K Rolett stability factor has been developed in the same analogy and manner using with s-parameters and it's valid only and only for single stage circuits.This is important and shouldn't be ignored.
For a cascaded/paralleled/mixed topology circuits, it will not be valid anymore.

As i understand the criteries of stability is reflected coefficients of the amplifier(in and out) must be less than one.
Can i design amplifier(with operating frequencies until 1GHz, for antenna) if in this range K<1 ?
Transistor that i've choosen has K>1 at 5.5 GHz and above. In range 0 - 1GHz it's not below 0.9, but not above 1.

K>1 simply means that the amplifier is stable at that given frequency regardless of its output and input reflection coefficients. That is, assuming your layout and bias conditions are identical to that under which K was derived. K<1 means that there exists the possibility of instability, if you choose certain input and output reflection coefficients.

Yes, often we are forced to design using devices which have k<1 over some bandwidth. This just means it requires extra care to make sure the final circuit is stable at all frequencies. Many RF transistors have K<1 at lower frequencies, this is often dealt with using feedback networks to kill the amplifier gain there.

That is we uses feedback network on the low frequencies instead of using K coefficient?
Is there any sense to use K In range until 1 GHz? (40MHz - 900MHz )
You've wrote "K<1 means that there exists the possibility of instability, if you choose certain input and output reflection coefficients" What can it be?(instability) Some fluctuations or...? Maybe overloaded, or it doesn't relate to it?
And last question, what methodics uses to stabilize the device when K<1?