Edit: Rule #1: never pound out an answer in a short period of time.
It's important to understand that how we think of light mathematically is quite a bit different from what light actually is in reality. "They're either like infinitely small bullets flying in straight lines, or they're like enormous expanding [3-dimensional] EM pond-ripples from a thrown pebble." (William Beaty, 2004.)
Polarization is the perception of those "pond-ripples" on a single plane. When you look through a pair of polarized sunglasses (glasses that permit those "pond-ripples" through a narrow region of the 3-D pond (ideally a single 2-D plane, but I doubt the tech's anywhere near that good)1 you're only seeing the photons that happen to conform to the polarizing matrix of the lenses. You're seeing some ripples, but not most or even all.
If you had a pair of glasses that were polarized to the same direction as your eyes, looking forward, but wrapped all the way around your head, you'd see the dark bands shown in your article about the bees. I'm unfamiliar with glasses designed this way, though, which is why no pair of polarized glasses I've used have produced the bands (I suspect they're designed such that the polarization reference is transverse to the plane of the lens and has nothing to do with which way your eyes are pointing).
The important point here is that light, itself, is only "polarized" artificially. In nature (as with our sunglasses), the bees eyes are designed to accept light along polarized lines, therefore accepting light along specific planes of the proverbial 3-D pond.
Why is this important? Because you appear to have not thought through the art of photography. People are rarely interested in taking an exact image of what they see (in fact, it's remarkably difficult to duplicate exactly what the eye sees). What they really want is something more idealized. In the professional/studio extreme this means that all shadows are controlled. The banding one of your articles refers to would be an undesirable distraction (like any other shadow we see today) that would be smoothed out with filters, diffractors, and all kinds of equipment.
At the other end of the spectrum are cheap cameras and amateur photographers — but even these want to minimize the undesirable effects to get that "ideal shot."
Finally, the photograph itself is reflecting light that's being perceived through polarized lenses. But the reflected light cannot reflect what the photograph depicts. If the camera has a polarized lens, it will show the kind of data you want to see — but the art of photography is to remove as much of that as possible.
Therefore, you need to make a choice. Do your characters want to see that polarized effect in their photographs or not? Do they, like we do ourselves, want all the distracting and extraneous shadows removed, to get the "perfect shot," or do they want something that's as close to what the eye sees as possible? (Which would be completely contrary to what we want to do today... please keep that very much in mind. It has nothing to do with whether or not we have polarized lenses.)
If they want the "perfect shot," your characters will be no more able to deduce things like the angle of light than we are today. (And we do analyze it. Forensics looks closely at imperfections like that to do exactly what you're thinking of.)
If they want "true to my eye" pictures, then they could deduce that kind of information.
1 Or the exclusion of some of the infinitely small bullets, it depends on whether you want to think of them as particles or waves. In relation to this discussion, it doesn't really matter which you choose. I chose the pond metaphor.