What is this type of hot plate and how do I use it?
I used to have an electric oven with similar hotplates and while I can't find a reference because it was such an old model I recall it was a safety cut-off. It would simply stop supplying power to the hotplate once a pot was removed, something you could easily confirm by seeing what happens if you turn on one of the hotplates without anything sitting on top.

As for the question of usage electric hotplates often don't use a thermostat, they use something commonly referred to as a "simmerstat". They simply control the duty cycle of the heating element, so in your example setting of three it would spend approximately 30% of the time on and 70% off.

I've tended to spend most of my life cooking with them and can't really think of shortcuts to learning how to use one effectively other than experimentation and getting used to them. For example I was just cooking some dried chickpeas and while I started things off at around 7/10 to bring them to the boil I later dropped that to around 2/10 and as liquid evaporated it ended up spending most of the time at 1/10 and that was still a reasonably rapid simmer for a small pot.