I still feel like I am in that category of Docker Dummy’s. 
But I see much potential with Docker and DSM6. Very easy upgrades, small compact hardware roll outs, ability to do load balancing, easy backup and system transfers, and more.
The web interface should be https://yourdomain.com. I have setup a sub-domain for my installation and a SSL cert to go with it. So mine is something like https://cms.domain.com.
I am not sure I follow on this. Are you saying that the cms-web container on the terminal window starts then stops? I think that is normal when it doesn’t have anything to do. If you are seeing the cms-db container start and stop, I saw that when I did not have the environment variables correct. I would delete your cms-db container, remove everything from the database folder, stop the cms-web container. Then rebuild the cms-db container, then start it. Look at the cmd-db log in docker and see if you see the main database being created. If that looks good and it is staying up, then I would start the cms-web containter. Look at the cms-db log again and see if you see that Xibo configured somethings. If that all looks good, then try to access the cms. If you cannot, please post back with any errors and screen shots of the docker info pages for the cms-db and cms-web containers.
Yes in the docker registry if you search for mysql, the first result should be “mysql”. I am currently using 5.7.18 that I selected when downloading the image, 5.6 should also work fine.