The fan you hear is to keep the microwave generator cool. It's outside the part of the microwave where the microwaves go.
Older microwaves had a fan-like metal stirrer inside the cooking box, that would continuously re-randomize where the waves went. This has been out of fashion for several decades.
> The reason some parts increase in heat faster is that they have higher concentrations of water;
Composition is part of it, but it isn’t the whole story. A microwave oven is a resonant cavity. There are standing electromagnetic waves in there, in several different modes. They have peaks and nulls. That’s why many microwaves have a rotating plate. It physically moves the food relative to the standing waves.
(I’ve heard the fans that you hear are there to reflect the micro waves and make them bounce all over the place but I don’t know if that’s true. Regardless, most models have a spinning plate which will constantly reposition the food as it cooks.)