Nimit,
1) "Nowadays mainstream physicists still believe that light wave travels (propagate) without using any medium to be carrier, i.e. it can travel by itself (via mutual creation between electric and magnetic field)!"
It is difficult to understand how such an absurdity was even considered. Every physicist was introduced to the theory of waves early in their education. In every case, whether the wave was propagating in a solid, a fluid or a gas, the solid, fluid and gas were the medium by which the wave propagated, otherwise the wave could not exist. Electromagnetic (EM) waves can propagate in solids, fluids and gases (frequency dependent).
Also consider that the medium itself is not propagating, it is the disturbance in the medium at some origin that creates the wave formation, allowing the disturbance at the origin to transfer energy through a wave action. A wave that propagates as a soliton is just a more efficient phenomenon of energy transfer by wave action.
Every medium, solid, fluid or gas, has permittivity and permeability. Contemporary physicists state that EM waves propagate through 'nothing', but this 'nothing' has permittivity and permeability. It is appropriate to add a "Duh!" here.
Now on to Einstein.
1) '...In this wider sense there does of course, exist an aether; only one has to bear in mind that it does not possess any mechanical properties...'
What in the world did Einstein mean by stating, "...it does not possess any mechanical properties...."? As far as I know permittivity and permeability have never been regarded as a "mechanical property" even in solids, fluids and gases.
Your Fig. 4. "Vacuum medium space-time" is applicable only for transverse EM (TEM) waves The TEM fields have no influence at a point in the direction of the axis of propagation until the wavefront of the EM field influence that is propagating as a wave gets to that point. Keep in mind that it is "assumed" that the influence in the transverse direction is propagating at the same velocity as the wave is propagating, which is why a propagating TEM wave is represented as having a spherical shape.