I'm going to take what I think is the main missunderstanding in your questions from which a number of your other errors stem.


A spherical wave is the same in any direction (remember: "Isotropy is uniformity in all directions" and "Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented" from your Wikipedia link), therefore it is isotropic.

Your missunderstanding is the phrase "all directions".

All directions means exactly that, ALL directions, not just all directions from a single point. It means all directions from all points. The "all points" is understood. Kind of like how in algebra AB is understood as one times A times one times B. When you learn algebra you learn that. When you learn about refraction you learn about isotropy. I suspect your mistake stems from an attempt to understand the term isotropic from the context of isotropic radiation discussed in the link I posted. If you had read further you would have also read

"An isotropic radiator is a theoretical point source of waves which exhibits the same magnitude or properties when measured in all directions. It has no preferred direction of radiation. It radiates uniformly in all directions over a sphere centred on the source. It is a reference radiator with which other sources are compared. Isotropic radiators obey Lambert's law."

But more to the point

"In reality, a coherent isotropic radiator cannot exist, as the isotropic radiator, with a radiation pattern (as expressed in spherical coordinates) of
http://en.wikipedia.org/wiki/Isotropic_radiator
would violate the Helmholtz Wave Equation, as derived from Maxwell's Equations.

You might want to look over Wiki's wave definition http://en.wikipedia.org/wiki/Wave
where it says "waves of electromagnetic radiation (and probably gravitational radiation) can travel through vacuum, that is, without a medium."
Which I already knew and is why I chose not to use the term medium in my OP.

Also read the wiki article "Field (physics)" http://en.wikipedia.org/wiki/Field_(physics)

Give yourself some time to mull this over but consider that your first replies to my OP were made 11 days after I posted and it is now 12 days untill the clock runs out on this thread. Stay on topic and we might get you to understand some things.