EM Plane wave, the changing electric field is in all directions right? I just want to confirm this, because this type of diagram seems pretty popular.
The electric field and magnetic field actually surround in all directions orthogonal to x axis, right? It is not just 2d pointing only in the y direction and z direction respectively.

 A: This is a fairly common point of confusion.  The arrows you see in that diagram express the magnitude and direction of the electric and magnetic fields on the $\hat x$ axis.
When you are introduced to vectors for the first time, they are usually represented as arrows which extend from one point to another.  The vector $\langle 2, 3\rangle$ is depicted as an arrow which starts on the point $(0,0)$ and ends on the point $(2,3)$.
This is nice and intuitive, but it implies that the vector extends across physical space, which it emphatically does not.  Vectors exist at isolated, individual points.  
Here is a "slice" of the electric field of an electromagnetic plane wave defined over the plane $z=0$, rather than just along the $\hat x$ axis:

Now imagine identical copies of this plane stacked along the $\hat z$ axis, and you have a picture of what the electric field from a plane wave looks like.  A faithful visual depiction would be far too cluttered to be useful, but this is the general idea.
For completeness, here's a slice of the field in the plane $y=0$:

A: The wave in your figure is linearly polarized with E along the $\hat{y}$ axis and B along the $\hat{z}$ axis.  That's built into the wave when it was created, and it stays that way.  You won't find any E along $\hat{z}$ or B along $\hat{y}$ for that wave.  
Some other wave might be different.  If could be linearly polarized along some other axis, or it could be circularly polarized.  A circularly polarized wave has E pointing in different directions at different times.
So no, in the wave you show, it doesn't surround the $\hat{x}$ axis.  But other waves could do that.
A: Yes, the fields are everywhere surrounding the direction of propagation. But it would be linearly polarized, in the same direction as the vectors in the figure. If one only draws the E-field vectors, it could be a representation like this: https://commons.wikimedia.org/wiki/File:Linear_Polarization_Linearly_Polarized_Light_plane_wave.svg
A: The EM wave in this diagram is just a ray, a geometrical visualization of the EM wave.
The EM wave is in reality a 4D wave, or at least you have to visualize it in 3D, where the wave rotates, that is, it goes from E wave to a M wave, because in the Maxwell equations, a moving E wave creates a moving M wave and this is how light propagates in the classical framework.
According to QM, the photon is the excitation of the EM field. So the E field creates an excitation in the M field, that creates an excitation in the E field, and that is how EM waves propagate in 4D.

