Windows and macOS have similar clients (Hass.Agent for Windows and Home Assistant for macOS).
I’ve found these kinds of clients useful because I can remotely wake-up or sleep computers, track how long they are turned on for, and automatically pause my lights and music when my webcam turns on.
It does. I use Mosquito but I believe HA has a built in one too. Mosquito was easy enough to set up though.
Honestly MQTT is like the nervous system of my HA setup. I started using it with Tasmota when I Tasmotised all my cheap WiFi bulbs, then opted for Zigbee2mqtt for my ZigBee setup.
But I also have things like my bedside clock (an old phone running WallPanel), my doorway tablet (a Nexus 7 running Fully Kiosk Browser), my PC and even my alarm clock app on my phone, all running through MQTT.
I even had Tasker on my phone communicating with HA via MQTT before I gave up on that. It’s really useful