Newton per meter (N/m)
Mathematically, Hooke's law states that: F = -kx, Where, x is the displacement of the end of the spring from its equilibrium position (in SI units: "m"); F is the restoring force exerted by the material (in SI units: "N" or kgms-2); and k is the force constant (or spring constant) (in SI units: "N·m-1" or "kgs-2").    
Hooke's law is not related to any "natural length". Rather, it defines a string constant: how much the string extends or compresses, depending on the applied force. In SI units, the spring constant would be measured in newton/meter.
I am not sure what you mean with "force constant". The SI unit of force is the newton.
It depends on the type of spring, but for general purposes the spring constant of materials, as long as it is linear, is the same in extension and contracting.
Spring constant of an elastic material is the force applied per unit extension.
It is Newtons per metre.
The ratio of force applied to how much the spring streches (or compresses). In the SI, the spring constant would be expressed in Newtons/meter. A larger spring constant means the spring is "stiffer" - more force is required to stretch it a certain amount.
The extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit.F = -kxwhereF is the restoring force exerted by the material (in SI units: N);x is the displacement of the end of the spring from its equilibrium position (in SI units: m);k is the force constant (or spring constant) (in SI units: N·m-1 or kgs-2).
Mathematically, Hooke's law states that: F = -kx, Where, x is the displacement of the end of the spring from its equilibrium position (in SI units: "m"); F is the restoring force exerted by the material (in SI units: "N" or kgms-2); and k is the force constant (or spring constant) (in SI units: "N·m-1" or "kgs-2").    
The SI unite of force is Newton (N)
The meter.
no the spring constant is not constant on moon because there is no restoring force there
In the SI system the radiation constant (Stefan-Boltzmann constant) is measured in W/m2.K4.
Hooke's law is not related to any "natural length". Rather, it defines a string constant: how much the string extends or compresses, depending on the applied force. In SI units, the spring constant would be measured in newton/meter.
I am not sure what you mean with "force constant". The SI unit of force is the newton.
larger the spring constant of a spring, the more stiffer it is.
2k