cable resistance and impedance

Resistance and reactance for a cable are both proportional to length, so yes - the resistance per meter is 1/1000th of the resistance per km.

The way you describe it, it makes no sense. First, describe the physical sizes, like how many wires, their material, sizes, distances from each other. What you want to use it for. Have not met a cable with 1 ohm/km. That is more like a busbar 1 meters on the edge, or some such. Reactance is frequency dependent. So start with a very good physical description and application. Then, maybe we see.

Actually, it does make sense, go to a electronics shop to buy some wire, the single cores (no matter how many strands or gauge) gives the wire R/km or R/M (R/meter)

For transmission line, say RG-58U Reactance, or some documentation has Impedance

http://www.benelec.com.au/pdf/coaxss.pdf

In general, no you can't. Resistance is linear for good insulation and short distances (and longer distances for single wires - I think you have a multiconductor cable). But you quickly get into characteristic impedances and length dependence.