I don't have an answer to your breastmilk question.

However, on the rest: Japanese security is IMHO and IME efficient and courteous. They speak a good deal of English, so don't worry that you speak little or no Japanese. On arrival, I believe you have to give digital fingerprints & photo, and they have a digital thermometer you walk past which is looking for fevers (goes back to SARS IIRC). Departure security screening is much like it is elsewhere, with WTMD and x-ray of your carry-ons.

Hopefully, other posters can chime in on the specifics regarding breast milk.