addons VS hassio-addons

If you have a broker set up in HomeAssistant it’s doesn’t really matter where that broker is as long as HomeAssistant is configured to use it and can connect. It sounds like it was hosted remotely, on paid hosting perhaps. I’ll hazard a guess since you mentioned lights that it’s using zigbee2mqtt so that addon will need to be setup too to use the same broker.

The HASSIO DuckDNS plugin can do it all for you too - https://github.com/home-assistant/addons/tree/master/duckdns

mosquitto is an add-on that runs as a docker container in the supervisor. It can be added and configured in the Add-on Store. The same can be done for NodeRed and Zigbee2mqtt. you could also add in some Zwave support to expand device compatibility with your smarthome.

Home Assistant add-on Almond on Github

Zwave here. ZigBee here, here, and here. ZigBee is a mess because it isn't tightly controlled like Z-wave is. Some devices work better with deConz or ZHA or whatever. I'm not really sure what works best with what, I avoid ZigBee for this reason (and a few others).

One thing that is throwing me off is controlling my z-wave devices. Prior to HA I have been using SmartThings which was working fine (minus the app switching). I integrated SmartThings into HA and the transition was seamless but I noticed that a lot of the HA integrations require Z-Wave JS.

I've posted https://github.com/home-assistant/addons/issues/1887 in this thread about issues with Mosquitto but references other issues I believe are related.

I installed the NGINX Proxy addon the other day and that seemed to go fine. Only problem I'm having is with some strange errors that keep occurring over and over.

Easy way would be to just create an automation that triggers on the temperature entity state. Then fire the mqtt publish service with it's value. You'll need to install the Mosquito add-on if you don't already have an MQTT broker set up.