Can microwaves change the molecular structure of food?
Yes. When you microwave a piece of chicken, energy from the microwaves causes the protein molecules to vibrate faster. This can break the hydrogen bonds and Sulphur bridges that give the protein chains their specific three-dimensional shape. With a piece of bread, a high enough dose of microwaves will cause the starch and protein molecules to break down and react with each other to create dozens of complex organic molecules.
When you put food under the grill, you are cooking it with infrared waves, which are part of the electromagnetic spectrum – just like microwaves. The difference is that infrared rays don't penetrate as far into the food. Most of the energy therefore gets deposited at the surface of the food, which gets brown and crispy. Microwaves tend to spread their energy more evenly throughout the food, so it cooks before the outside becomes brown, but the basic chemistry is much the same. There are no chemical reactions unique to food cooked in a microwave.
However, microwaves emit non-ionizing radiation; a type of radiation that has enough energy to move atoms around within a molecule but not enough to remove electrons. Because the radiation from microwaves is non-ionizing, it can only cause molecules in the food to move.
Although there is no clear evidence of harm, many people are concerned that low levels of electromagnetic radiation may impact human health over a long time.