No, that is incorrect. Domestic to international connection in Japan baggage will be through checked at the origin airport, given that the connection meets minimum connection time at the specific airport and two airlines involved have internline agreement.

In OP’s situation will check-in at JAL at KIX and baggage will be checked all the way to LAX and OP will not see checked baggage at HND.

It is correct that at HND domestic and international terminal is separate. Upon arrival at HND OP will take free inter-terminal bus from domestic Terminal 1 to international terminal. At international terminal at HND there will be passport control where OP will receive a stamp on a passport.

Also, to OP you mentioned both KIX-HND domestic and HND-LAX are in business class. JL domestic 737s do not have business class. Have seen so many people making wrong assumption here at FT. OP will be flying on Class-J on KIX-HND portion and it is domestic premium economy product. “J” on Class-J comes from “Japan Airlines” but I think all those confusions comes from letter J is used for business class fare code among airlines. There is not much of service on short KIX-HND portion to begin with but OP will receive bonus miles as premium economy on KIX-HND portion, not business class bonus miles on KIX-HND portion.