Where are old Himawari weather satellite images available to the public? Is the 18-Dec-2018 Bearing Sea fireball still there?
You need to go this site - Himawari Archive and then it depends on what category of user you are and then obtain the imagery that way. 

UPDATE -

On OP's request I am recording the information I got from JMA when I wanted to access Himawari's images. You need to specify what kind of user you are 

a) research
b) commercial.

Presuming research you can obtain Himawari images from the following institutions as mentioned in the original link I provided


  The following four Japanese institutions operate Himawari-8 data archiving and redistribution services on a best-effort basis for research, development and education:
  
  1) JAXA Himawari Monitor (Japan Aerospace Exploration Agency)
          http://www.eorc.jaxa.jp/ptree/index.html
      Himawari-8 Data Download and Processing System (Data Integration and Analysis System Program)
  
  2) http://himawari.diasjp.net/expert/
      Center for Environmental Remote Sensing (CEReS)
  
  3) Chiba University
          http://www.cr.chiba-u.jp/databases/GEO/H8_9/FD/index_jp.html 
  
  4)    Himawari Satellite Project (NICT : National Institute of Information and Communications Technology)
          http://sc-web.nict.go.jp/himawari/
  
  Users must register to download data from each institution and observe the individual data usage policies. 


If you are asking how I would do it then I must mention I use a python software called
SatPy 

Then I go to this URL - JAXA FTP URL( I think it is only visible if you are registered) and then download the data for whatever year I want. Then write a small script using a SatPy reader and view the data. 

NOTE For the last points you are better off asking questions either on SatPy and for the data itself writing email to JAXA.