thanks for trying the docker.
With MQTT, there is a file created called mosquitto.conf with line 20:
allow_anonymous false
Change this to true if you do not want passwords.I was sure that if the passwords.mqtt file was empty then it would allow anon access. Will check.
Re HA stuff
I use my Node-Red and MQTT dockers together. I try to get as much as possible into mqtt directly (various ESP8266 devices) if I can. If not, I use Node-Red to transform the other devices (Hive thermostats - Tado Thermostats & Ciseco sensors https://www.wirelessthings.net/things/sensors) into MQTT messages. That way, I can try various HA applications at the same time: Domoticz, Emoncms, Home-Assistant, OpenRemoteCommander etc without problems.