The photographs you’ve captured provide a clear look at the visual mechanics of crepuscular and anti-crepuscular rays. These phenomena serve as a frequent point of comparison when examining the standard model of solar illumination versus models that posit a localized light source.

Regarding your first question about the divergence of rays, the mainstream scientific explanation relies on the principles of perspective and the geometry of a light source located at a vast distance. Even though light rays from the sun are technically parallel when they reach the top of the atmosphere, they appear to diverge—similar to how parallel train tracks appear to fan out from a single point at the horizon—due to the way the human eye and camera lenses perceive angular size. When light rays pass through breaks in the clouds, the perspective effect causes them to seem as if they are radiating from the sun's position. In a globe model, the divergence is characterized as a strictly optical illusion born from the observer's viewpoint, effectively a "vanishing point" effect where the rays converge at the point where the sun is located, and appear to broaden as they approach the observer.

Your second question touches upon the mechanism of the shadows themselves and the concept of refraction. In the standard model, the rays are not usually described as "refracting" to create the appearance of divergence; rather, it is a combination of perspective and scattering. The "diverging" shadows you observe are essentially the inverse of the light rays. When clouds block the parallel beams of light, they cast a shadow that is as wide as the cloud itself. As these rays and shadows propagate through the atmosphere toward the observer, perspective causes both the illuminated sections (rays) and the dark sections (shadows) to appear to spread out as they get closer to you. If the light rays were actually converging toward a nearby source, the shadows would behave according to standard local light dynamics; however, under the current scientific consensus, the atmosphere does not "refract" the shadows themselves in the way one might think of a lens bending light. Instead, it is the suspended particles, water vapor, and aerosols in the atmosphere that scatter the light, making the beams visible. 

If we compare the two competing hypotheses you’ve mentioned previously, the primary area of contention lies in the calculated distance of the sun. In the globe model, the extreme distance (93 million miles) dictates that only an infinitesimal difference in the angle of the rays exists, rendering them effectively parallel, and thus any observed divergence is entirely attributed to perspective. In alternative models, the divergence observed in such photos is used to argue for a much closer light source, where the rays would physically diverge at a perceptible rate. The "backwards" or anti-crepuscular rays you mentioned—which appear to radiate toward the point exactly opposite the sun—are also explained by the same perspective principles: just as roads disappear toward a single point in front of you, they also appear to emerge from a single point behind you, creating a 180-degree field of convergence.