It'll be a switch mode power supply, where the power is rectified, converted to high-frequency AC (50-200 kHz), then sent through a certain specialized transformer.
The other problem they create, then, is high frequency noise which must be filtered out. Some cheaper adapters just dump the noise back into the mains and cause problems for _other_ devices.
Come to think of it there's a decent chance it's a /different/ adapter somewhere on his system that's causing the problem and not the size or capacity of the products native adapter.
There absolutely is. The core material is not iron, it is a material specifically engineered for the purpose. There's a very specific size gap between the two halves of the core. There's an extra sense coil for the feedback circuit.
The gap is controlled by the cross section of the core but also contributes to EMI. The sizing concerns are typically related to the latter problem.
An SMPS can easily use an external feedback circuit and may do so for certain types of applications. For mass manufactured low current applications you can often buy them with one integrated.
Unfortunately I'm unable to find any examples of them used outside of voltage-multiplying circuits in obsolete electronics.