>>>...I'm going to have to do four upgrades; one to 5.2, then to 6.1 and finally to the latest version...
Correct.
>>> Are there any docker-compose images corresponding to 5.2 (201707-GA)and 6.1 (201901-GA)
If you are looking for Alfresco-packaged images, that didn't start until 6.0. You should be able to find 6.1 images. Check Docker Hub and if that doesn't work, look at the tags on the Alfresco Community Packaging project.
>>> Our original database is MySql rather than Postgress, and we'd like to move to MariaDB
MySQL and MariaDB are compatible so it should not be a problem to move from MySQL to Maria. Many folks run Community Edition on MySQL/MariaDB rather than PostgreSQL, so it isn't a concern.
>>> The documentation says that the docker-compose solution should only be used for test, but what are the reasons for this?
As far as I know, this is an Alfresco Support hedge statement because they only support K8s in production.
With that said, so far, all of my clients have chosen to just manually install 6.x and run it in traditional, non-Docker deployments, and that is a mix of Enterprise and Community installations.
In non-prod environments I have seen no problems running docker-compose, even for long-running servers.
