How exactly is food heated? Do microwaves penetrate all the way inside or do they heat only the surface layer?
This is a complex problem because the penetration depth, intensity to drop by 1/e, depends on the frequency, relative permittivity and conductivity as
$$D=\frac{0.225 \lambda}{\sqrt{\epsilon_r}\sqrt{\sqrt{1+\tan^2\delta}-1}}$$
where $\tan \delta =\frac{\sigma}{\epsilon_r\epsilon_0}.$
The absorbed power is $P=\sigma |E_i|^2$ but the intensity in the food $E_i$ is a complicated function of the illumination and material properties. Even heating a cup of water results in a nonuniform heating that only equalizes by stirring or conduction because the field penetrating the water is not uniform due to these losses. The more complex the food is in its $\epsilon$ and $\sigma$ the less its uniformity as the field penetrates.
The 915MHz oven of days of old was just as prone to uneven heating as the newer 2.45GHz one despite its 2.6$\times$ longer wavelength.
Why soup takes longer to heat? Because of water transparency to microwave and low heat transfer or because of higher heat capacity?
Water has high permittivity (smaller penetration length) and high heat capacity, both would imply longer heating time.
Why it is better not to place food in the center of the rotating plate, but rather let it perform a circular trajectory with the turn-table - because of the nodes of the standing wave, despite the highly irregular form of the object inside the microwave?
The design of the cavity dimensions aims to maximize the number of modes that can simultaneously exist in the band $2450\pm50\rm{MHz}.$ More standing waves, modes, the more uniform is the field within the cavity. Unfortunately, the presence of the food (life is hard sometimes) with its varying, rather unpredictable properties, detunes this theoretical arrangement and nodes or low intensity locations may develop. To make it more uniform, in addition to the rather common rotating glass table holding the food, in the waveguide that illuminates the cavity a rotating wave "disperser" is sometimes placed. These unpredictable mode structures that develop has another rather unfortunate effect, namely the increasing reflection back to magnetron can both detune it and lower its output power. I have not heard that any commercial oven would be using an isolator to overcome this problem, probably because of the prohibitive costs of a 1kW/2.5GHz isolator with its additional weight and size. The glass plate holder, be it rotating or not, is needed to have some absorber if the user were to forget to load the cavity; otherwise the tube might blow up from all the reflections.
In a theoretical analysis of a typical domestic microwave oven cavity with dimensions $342(W) \times 195(H) \times 357(D) \rm{mm}^3$ and the turntable diameter about 325mm, the cavity had 108(!)modes and despite of that the field was still fluctuating 30dB at $100\rm{mm}$ above the bottom! When rotating it most points will fluctuate about $\pm3\rm{dB}$ but not within ~10mm of the center where it can still have 10dB variation according to the simulation.
