Once again, all you never wanted to know and more:
Microwaves are electromagnetic waves, as are radio waves, infrared waves and visible light. The difference between all of those types of waves is simply their energy. In the examples listed, radio waves have the lowest energy, microwaves the next lowest, infrared after that and visible light has the highest energy. Not exactly what you'd expect, I know!
Why aren't things cooked by visible light? The reason is that very little of the light interacts with the objects we see and it's lucky for us, as our eyes are made for viewing the light which is reflected. The colour black absorbs the most light and white reflects all colours (ie energies), as you probably have learned at a young age walking with barefeet quickly across a blacktop road to the cool white cement of the pavement.
Radio waves, the lowest energy waves of the four, are all around us. They don't interact with anything in us and we don't reflect them. The waves pass right through us.
Infrared waves are what you might think of as "heat" waves. They interact with us, they heat us up. The sun heats the earth this way. A fireplace warms two cozy people (or, in this discussion, one cozy person and one too-warm harried person chasing a much younger person away from the infrared source so as to prevent a trip to the burn unit) this way. Infrared radiation is absorbed by almost everything and, therefore, heats almost everything up!
The microwaves our microwave ovens produce, in contrast, can interact with water, fats and sugar. They are not completely absorbed by them and the majority of the waves pass through the food without interaction. Those that do get absorbed heat up the food by heating up the water, fats and sugar.
The hots spots are caused by the unabsorbed microwaves bouncing around the inside of the oven. (The metal "cage" keeps the microwaves in by reflecting them back into the oven, just like a mirror reflects visible light. It's not necessary to have a solid cage to keep all microwaves inside. The reason for this requires a slightly more technical discussion, but if you're interested... ) Back to the hot spots! We've got our unabsorbed microwaves bouncing around, right? Microwaves are waves and can interfere with each other just like waves of water. Have you ever scooched back and forth in a bathtub to make a tidal wave? It takes a few times to get the wave up to a decent size. That's constructive interference-- you're constructively interfering with each wave to make the next one bigger than the last. Same analogy, but with second thoughts. Have you ever, at the last minute, decided that you didn't want a load of water on the floor? What did you do? Probably wait for a second and then make a wave against the oncoming wave. Everything slowed down (hopefully it was enough!). There you go, destructive interference, you just stopped a wave with another wave. Same thing in a microwave, except that it's the reflections off of the sides and the source making the waves. Some constructively interfere and give hot spots and some destructively interfere to give cold spots.
Regarding leakage from microwaves: microwave radiation interacts with water, we're all made with loads of water, so you'd know it if there was any leaking! Also, microwaves have absolutely nothing to do with nuclear radiation, unless it's in the very indirect sense - if the electricity powering your microwave comes from a nuclear plant.
Umm, I'm open to any questions if anyone has read this far. And has a question, I guess.