KIX -> HND on JAL domestic 737, HND -> LAX on AA 787, both business class.

Since KIX->HND is a japan domestic flight, do I get my passport stamped at HND (or KIX)? And do I take my luggage out at HND and switch terminals at HND and re-clear security? I have perhaps 2.5 hrs at HND until 1am flight to LAX. I heard HND is a great airport, so I hopefully won't have to waste time on clearing immigration at HND so that I will have time to check out all the amenity at HND.

By the way, how does AA serve meals for the 1am flight? I hope they wont make you eat a full dinner after 1am. So I am guessing light snack after takeoff, and then full dinner 2 hrs prior to 7pm arrival at LAX?