Are electromagnetic "plane" waves measurable or just a virtual concept? I find plane waves are uncompatible with light cone.
Perhaps plane waves are "virtual" and can never be measured
in that case, shouldn't we call plane waves as "virtual plane waves"?
(other option could be that plane waves allows waves travel faster than c)
I would like to clarify this point through this question.
If plane waves would exist(as measurable), then higher than c speed 
could be reached like this:
A wave going from X to Y at a speed c, it will reach Z at higher
than c speed, because it will reach at same time, traveling more distance.
                   (X).
                    |   
                    v   
                  ________________________________________________  
plane waves       ________________________________________________  
going X to Y      ________________________________________________
                   (Y).                                       (Z).

In a real situation the wave will be a circle (or a sphere in 3d) 
so it will get Z later then that's not a plane wave.
 A: A plane wave $e^{-i(kx~-~\omega t)}$ is a case where the Fourier transform of the wave is delta function of momentum.  The physical reality of a plane wave is then somewhat more in line with a mathematical “fiction.”  Usually there is some envelope with the wave, such as a Gaussian packet, which attenuates the wave off to “infinity.”  However, the plane wave is useful for waves with well known momentum, or a small spread or uncertainty in $\Delta k$ or $\Delta p$.  Further, one can write a plane wave as an infinite sum of Bessel functions.  The wave as it interacts with a hole in a screen selects out some of these components by Kirchoff’s rule, and the wave at the other side of the screen is a spherical wave front. 
A: The questioner is considering point sources. If you consider a source that is planar, you will find that, at least near the source, it produces plane waves. Of course this is all just an approximation, but, since all experiment has accuracy limitations, everything in physics is an approximation.
A: A "plane wave" generally refers to an infinite and perfectly flat wavefront, which cannot exist in reality, of course. However, there is nothing at all impossible about a plane wave of finite extent. Such a wave will experience diffraction at its edges, of course, but can still propagate over long distances before losing its planar nature.
The problem with your question about faster than light information transmission, is that if X were the only point emitting a wave, then it would be a spherical wave, not a plane wave. A plane wave can be thought of as being composed as a superposition of spherical waves emitted in phase from every point on an infinite plane. So in your example, information would not be arriving at Z from X, but instead from some other source point within the causal past of Z. In your diagram that point could be at the same height as X, but directly above Z.
Considering a wavefront (planar or otherwise) as a superposition of spherical waves is the central feature of the Huygens-Fresnel Principle, which would be a good reading on the topic.
A: As soon as your source is X, there is no wave propagation from Y to Z, whatever wave front looks like (spherical, plane, etc.).
About "virtuality":
A wave is real if it is of sufficient intensity, i.e., it consists of many-many photons. Then your detector at Y will work as well as your detector at Z.
For a low-intensity wave it is not the case and the wave describes the probability amplitude. If you have only one photon in it, only one detector will register it.
