I'm looking for a way to see the contents of the requests the Docker CLI makes to the Docker Daemon for image creation, container creation etc. Is this possible to see, and if so, how?
You can run the docker daemon with debugging enabled which will show the URL being requested, but not the contents of the request. In /etc/docker/daemon.json, you can configure debugging with:
{ "debug": true }
Then restart the service. On systemd based systems, you can see the logs with journalctl -u docker.