No. a wave emanating from a point source in an isotropic medium could be seen as a sphere (with its electric and magnetic components at right angles to the propagation direction, which will be a radius out from that point. But a wavefront from a more complex source will be made up of contributions from all over the source.
and that’s without all sorts of other complications that Real Life brings in. Like non-isotropic media (crystal optics is FUN!)
And we haven’t even brought in adding Coherent Light vs. adding up Incoherent light. In the Real World, of course, all light is Partially Coherent, and you have to use the Van Cittert-Zernike Theorem. And isn’t THAT a lot of Fun?
But, yeah, in the simplest – simplest – cases you can get away with modeling it kinda like a sphere.
No, that’s not how it works. In some sense the sideways extent is related to the uncertainty in the wavelength, but even that is going to send you to false mental pictures.
Technical aside, in case you’re interested: You can’t actually have a spherically symmetric EM wave. It’s not a valid solution to Maxwell’s equations. (You can if you don’t care about polarizations, but that washes away the crux of the physical picture being discussed, so it would be a cheat here.)
Birkhoff’s theorem is the proximate explanation, but, yes, it’s about the interplay between vector fields and spherical symmetry like the hairy ball theorem.
Pasta’s point is that light cannot propagate spherically. A simple way of thinking about this is to take a point source and observe that you cannot accelerate it in a spherically symmetric manner to produce spherically symmetric em waves.