Is git required for docker, or can you use another VCS, specifically hg (mercurial)? If I want to use that instead, what sort of changes do I need to make?
AFAIK git isn’t required for using docker. But I think you need a github account for automated builds on docker hub,
There is support for Docker Hub Automated Builds against GitHub and Bitbucket, though that’s mostly for convenience; anyone can push from anywhere using any kind of CI/CD or manual process.
The docker engine itself doesn’t require any source/version control.