In microwaves - you heat up food really fast. Is it true that microwaved food will cool down faster than oven heated food? Someone told me "if it heats fast, it will then cool fast."

No. Microwaves cook the food in a very different manner than normal thermal heating, but microwaved food has the same thermal energy that it would have if it had been warmed by more traditional methods. Microwaves heat food by exerting torques on the individual water molecules in the food. These molecules jiggle back and forth and sliding friction between them heats the food. This peculiar route to energy addition explains why frozen portions of the food don't heat well: the water molecules are rigidly oriented and can't jiggle back and forth in order to become hot. But despite the fancy heating scheme, the food retains no memory of how it was heated. Once it is uniformly hot, it cools at a rate that depends only on how heat is transported out of it. Microwaved food cools just as slowly as normally cooked food.

Which electric light bulb is best for the money, i.e. uses least electricity and has greatest light. I remember my high school physics teacher saying something like 50 watts -> 100 watts doesn't double the light, just eats electricity.

For a given type of light bulb, the higher wattage bulbs are more energy efficient. Each light bulb has some "overhead" of wasted power that goes into heating the supporting structure and glass envelope. The higher wattage bulbs produce a little more light per watt of power. But not all types of bulbs are equally efficient. Long life bulbs are the least energy efficient because they run cooler than normal bulbs. The filament lasts a long time, but wastes more power producing infrared light. Some "energy miser" bulbs aren't as good as normal bulbs. They may have lower wattages (typically 55 W instead of 60 W or 90 W instead of 100 W), but they actually produce significantly less light and thus consume more watts of power for each unit of light they produce. The most efficient incandescent bulbs are halogen lamps. These lamps, with their chemical recycling process, run substantially hotter than normal bulbs and produce more light per watt. They also last longer than normal light bulbs. They also produce whiter light (less red) and are just plain better bulbs than normal light bulbs. They cost more money up front, but it's worth it in most cases.

On a three-way lamp, what are the switch settings for? Does it pump in more energy?

The lamp has four switch positions: off, filament 1 on, filament 2 on, and both filaments on. The bulb has three electrical connections to its filaments. One contact delivers electrical power to filament 1, another contact delivers electrical power to filament 2, and the third contact returns electricity from both filaments to the power plant. The switch carefully controls the flow of electricity to the two filaments so that at the low light setting, only the small filament is on, at the medium setting, only the large filament is on, and at the high setting, both filaments are on.