Hi Paul,
I'll take a stab at answering a few of your questions.
Photo Date: Translations of the book in the Japanese National Archives show it was published in October 1935. How could a picture supposedly taken in 1937 possiibly be in a book published two years earlier? Of course I'm assuming the translation(s) were accurate. As far as I've heard so far, there's no hard documentation on date of construction of any of the port facilities. Pictures seen on forum so far aren't conclusive as they don't show enough detail.
Different Clothing Than on Takeoff: Undoubtly they had changes of clothes. Remember, though, Howland Island was only intended as an overnight refueling stop. Different clothes the next day probably. In all the pictures of AE and FN seen at the various stops before Lae, I've never seen one with them in "whites".
Amelia's Hair Too Long: Look at her hair in the film of them boarding in Lae. Very short, up off the neck, shirt collar. It couldn't have grown that much in a day or so.
Not Enough Fuel: There are written records from the day of the flight detailing what was put in the tanks.
Lack of Guards: If they had been 'captured' then any authorized pictures would also show them as under guard/surveillance. If it was a rescue, same thing, to show what 'good guys' we are. Unauthorized pictures might be another story but I'd think access to the dock would have been controlled from the time the authorities knew the ship was approaching the dock. Even in 1935-7 the Japanese were fanatic about security.
Photo Not Close Enough/Posed: Eye of the photographer and what he or she was trying to record. Overall view of the port activities -- people not that important. If the people were important enough to record their arrival the photographer would have tried for a shot which would prove identification. The photo tells me the photographer wasn't that interested in the identification of the people. Were there other shots? Impossible to know.
The Plan: Don't know if she said it or not. Ric will have to address that. Don't know exactly what maps Fred may have had on board. The map used by the Colorado/Lexington search effort didn't extend far enough south to show Gardner. Watch Ric's video from the New England Air Museum for details.
The Search Party: I don't think the sextant would have been much good as a signaling device. The compact might be better. If they were awake when the Colorado's search plane flew over and they heard/saw it, maybe she did signal. If so, it wasn't seen.
The Radio Transmissions: Judging from the pictures shown in the HC program, I don't think the aircraft would not be able to make any kind of landing which would have left it capable of sending anything. Tides would be different; many, many miles away from Gardner/Howland. Koshu deck logs from time in question still exist. Ric has commented on them earlier. She was nowhere near where the picture was taken, when it was supposed to have been taken in 1937.
These are some random thoughts from me.