Believe the missing windows are allowances for ducting for the sidewall risers...feed the airconditioning...this area is not as insulated and may account for the cold sink area that corresponds to this general area.
did many starts on the apu at high levels & yes at FL410 too on the NG's on ETOPS flights. no problem at all & it starts all the time well at least in my own experience.
There's only one airline that I'm aware of that is approved to fly ETOPS without the apu running on a 737NG. Does your airline start with the letter A?
Doesn't means he's AS. There's a KAL flight from Seoul to Urumqi where only a small portion of the flight is ETOPS and you don't start the APU until later in the flight. Probably others, as well.