are SPP's (surface plasmon polariton) without apply light? if yes: Is it moving along the x axis? and How is light coupled to SPP's with a frequency equal to plasma frequency?
Not sure what you are asking. The SPP moves in whatever direction you define it to move, but it is always in a direction in the same plane as the interface. For a simple introduction to SPPs, check out Lecture 21 here:
http://emlab.utep.edu/ee5390em21.htm
There are electronic notes and a recorded lecture on YouTube.
Well they do not need additional light, but remember that an SPP is essentially a photon coupled to an electron oscillation at the surface of a metal. Can an SPP propagate without light? It is light.
Because SPPs can be considered as proper modes of metal-dielectric flat interfaces degenerated with respect to propagation directions, they can propagate in all directions depending on excitation conditions.