The way I understand it. (and here I'm just telling you what I have heard from other people) is that the brick we use has two layers. So going from the outside to the inside the structure is: layer1, layer2, graphite crucible, metal to be melted.
Layer1 is thermally insulating. Keeps the heat in the brick. It is still 300ish celsius at the end of the melt, and it increases further as the whole structure "cools".
Layer2 "captures" the microwave radiation and is the thing the microwave oven heats. All that energy is captured inside the brick and layer1 doesn't let it out so it heats up very quickly.
And then layer2 heats up the crucible via mainly heat conduction (so the interface has to be neat between them) and only to a lesser extent via heat radiation.
The main dangers of the operation is the same as with any other process which results in tens of grams of molten metal. Those would be not new to anyone who casts metal. (But entirely outside of the experience of someone who never worked with molten metal before.) Everyone with normal household experience would know that molten metal is hot, what might surprise someone without specific training or very good intuitive grasp of physics is that if it contacts water the water immediately turns into steam and that will make the molten metal fly everywhere. [1] So that would be the first unexpected turn of events. Hopefully you have a bucket of sand ready to put out the resulting fire, because water is not your friend in this situation.
It is also important as you pack the crucible to not form a "bridge" between the walls with the metal. Because before the metal melts it expands. And if you pack the to-be-melted metal too tight it will crack the graphite crucible. Which would ruin the brick.
Then the other surprise is that the layer1 keeps heating up even after you have removed the brick from the microwave. (because layer2 is very hot, and that heat is slowly dissipating through layer1) And if you use the brick too much without letting it cool down between melts it might crack, or it might crack the glass plate of the microwave.
