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You can use docker inspect command to dump any meaningful info about the running containers. You can get details about networking, images etc.
Also you can check systemd units (or whatever your system uses) in case they are used to launch containers or docker compose files.
Running ps you should also be ablen to see if docker-compose is used, and in general this uses standard names (docker-compose.yml/.yaml), so you can simply find / -name those.
Here ya go: https://github.com/Red5d/docker-autocompose
Looks like a really interesting project, might need to tell a few people about this
Well you can at least connect to the running container with a shell and see what processes are running, and maybe copy some binaries and config out of it into the local file system.
You can also use $ docker inspect to get some more info.
docker inspect <container_id> tells you everything about the container in json format.
The other comments on this thread had nailed it down but there may be some commands you will need as well, so the command "history" has a journal of what command was ran at what time.