Years ago, I saw in a Navy Technical Publication that had both English and Metric Units that a rope needed to be 300 ft (91.4411 meters) long! What?! That will turn anyone against the metric system. A little change in humidity will alter the rope several feet! And they gave the length to a tenth of a millimeter! Stupid and that kind of stupidity keeps us in the English system. A 300 ft rope is 90 meters long, and probably 100 meters would work! For most things that we work with 10% error is acceptable. If a politician goes for the metric system, their opponent will shoot them down for votes!

No.
The Nikon 28-300mm F3.5-5.6 is a FX lens. A real good all around walk around lens. For the DX squad, there is a 18-300mm Nikon lens you may enjoy. Both are VR.

The snow in the foreground is dark, so distance to the flash is not the reason. I am assuming an on camera flash or near camera flash (reflection of the light in the rabbit's eye). As we all know, snow is from snow flakes, a flat crystal of water. Take a bunch of coins (or poker chips) and toss them onto the floor, even a deep pile, and most will orient themselves near horizontal. Same for snow flakes. The camera was a a low angle, so the majority of the light that hit the snow was reflected up and away from the camera.

Yes, the manual may say 32F for the low operating temp. I have used Nikon D300s & D600 for hours outside in 0F weather w/out any trouble! I have read that -40F sometimes the display is slow, but not damaged. Yes, in cold, batteries drain and keep a spare in an inside pocket.

I think the only danger is condensation freezing on mechanical parts. Put the camera in a bag before you go inside, then wait until the camera is at room temperature before doing anything with it.

I have used a Canon Rebel in -40F in 180mph wind (windchill -100F) without any problem. Exited plane at 30,000ft, camera lens had frost when I landed because of the very cold camera in the lower warm air, but no problems.