Sounds made up to me. Only a few intelligence and commanding officers would have known the bio of the Japanese commander, and they wouldn't have had much reason to capture him.
Agreed - particularly having been on the island for a month. Those guys (whether they knew who he was or not) weren't in the mood to tell some Japanese guy what a great man he was at that point, I'm guessing.
When you're afraid to fall asleep, you get a little jumpy.
They even had to make up ways to call a medic ("Tallulah!", because of the pronounciation, so the enemy couldn't imitate them and take out their docs) - so it's a pretty good stretch to think they'd be sweet talking this guy.