The P-51 that crashes onto the island in 1944 had black and white stripes on its wings-these were known as "Invasion Stripes," and were used for a short period after the D-Day landings in Europe and not in the Pacific theater.
Although Northern Lights aren't visible in the southern hemisphere, it could have been the Southern Lights. It is more likely however that the lights and Skull Island's unique storm system are due to the 'hollow earth' characteristics which are never fully explained.
When the the soldier plans to sacrifice himself with the grenades he pulls the pins and releases the spoons, this sets the 5sec timed fuse. There was more than 5sec from arming to detonation not to mention the blast was way to large.
Photographer was shown loading Kodak Plus-X film into her camera, which is, or was, a mid speed black and white film, OK for daytime shooting, but not for low light shots as she is seen taking later, at least not without camera shake and blurring or unless you use flash equipment. Also, as it is black and white, it isn't what you would use to capture the colors of the Southern Lights and a timed exposure would just be a bunch of grey blur.
The Japanese soldier was holding a German Mauser pistol. Although Japanese forces would not have been able to obtain additional munitions at the end of WWII due to financial issues, the munitions they already had would still be in circulation.