I concern myself with the validity of my interpretations of (b).
Here I am more confident slightly. The divergence of the current density is merely $- d \rho / dt$, so as there is charge flowing through the wire the magnitude of the current density ought to only be non-zero within the wire.
The divergence of the electric field is only non-zero at point charges. Given that it seems weird for points in the wire to be sources of divergence in the electric field if they're constantly moving, I reckon the only charges I can use is the electrons of the wire (bound charges?) not shot through the wire as a current which should be at the surface, but this seems a bit weird to me as if its a bound charge it seems weird for me if it is at the surface as that tends to be a thing free charge does as it has the freedom to do so while bound charge doesn't (as free charges can move themselves however they must to balance out the field while the bound charges more or less stays where it is but becomes polarized).
Where am I going wrong in my interpretations for (b)?