First, a hat serves as insulation against convective heat transfer. By trapping a layer of air near your skin, it slows the movement of air and heat away from your head. But it also acts as a barrier to thermal radiation. Just as a tree overhead radiates heat toward your skin and keeps you from losing heat to the dark night sky, the hat on your head radiates heat toward you and helps to keep you warm. On a sunny day, it keeps you cool by blocking the direct transfer of heat from the sun to your head.
Aluminum may be a good conductor of heat, but its a terrible emitter or absorber of thermal radiation. When you wrap food in aluminum foil, you dramatically reduce that food's ability to lose heat via radiation if it's hotter than its surroundings or its ability to gain heat via radiation if it's colder than its surroundings. Aluminum foil doesn't have much effect on heat transferred to or from the food via conduction or convection because aluminum itself is a good conductor of heat.
Whenever water is exposed to air, the water and air begin to exchange water molecules. By that, I mean that water molecules leave the surface of the liquid water to become water vapor in the air and water molecules that are already vapor in the air leave the air to become liquid water. If the relative humidity of the air is less than 100% (meaning that the air can still hold more water vapor), more water molecules will leave the liquid water than will return to it and the liquid water will gradually evaporate into water vapor. If the relative humidity of the air is greater than 100% (meaning that the air is holding more water vapor than it can tolerate), more water molecules will return to the liquid water than leave it and the water vapor will gradually condense into liquid water.
For a water molecule to leave the surface of liquid water, it needs a substantial amount of energy because it must break several hydrogen bonds which are holding it to its neighbors. It obtains this extra energy from nearby molecules and they become colder. Whenever a water molecule returns to the surface of liquid water, it returns this energy to the nearby molecules and they become hotter. Thus whenever liquid water is evaporating, the water molecules that leave the liquid water are taking away its energy so that it becomes colder. And whenever water vapor is condensing, the water molecules that return to the liquid water are giving it energy so that it becomes hotter.
When your skin is wet and water is evaporating from it, your skin also becomes colder. Blowing additional air across your skin prevents any build-up of humid air near its surface so that far more water molecules leave your skin than return to it. The evaporation then proceeds rather quickly and your skin feels quite cold.
The answer depends on how cold you allow room temperature to become. Without a heater, the water temperature in the bed will be very close to room temperature. When you then lie on the bed, you will be in contact with a surface that's at room temperature and heat will flow out of you and into the water. Your heat will warm the water and it will tend to float upward and remain at the top surface of the waterbed, forming an insulating layer that will slow your heat loss. However, heat will continue to diffuse into the water as a whole and you will continue to lose heat. As long as the water isn't too cold, your metabolism will be able to replace the lost heat and you'll stay warm. But if the room and waterbed are very cold, your temperature will begin to drop. I'm not sure how cold the water would have to be for this to happen, but if the room and water were almost ice cold, you'd probably have trouble.
A vacuum or "Dewar" flask is a double-walled vessel with a vacuum between the two walls. It's effectively a bottle inside a bottle, with their only contact at their mouths. Since there is no air in between their bodies, no heat can flow from one bottle to the other by either conduction or convection. The only way in which heat can move between the bottles is via thermal radiation. By coating the surfaces of the two bottles with highly reflective materials such as aluminum, even thermal radiation can be almost prevented from transferring heat between the bottles. Since there is virtually no way for heat to flow into or out of the vacuum flask, except through its mouth, the flask can keep hot things hot or cold things cold for extremely long times.
You can prevent heat from moving about with the help of insulation. The three principal mechanisms of heat transfer are conduction (the passage of heat through a stationary material), convection (the passage of heat in a moving fluid), and radiation (the passage of heat as electromagnetic waves or light). Good insulation doesn't conduct heat well, doesn't support convection, and blocks radiation. Wool is a good example: its hair and trapped air don't conduct heat well, the trapped air can't really undergo convection well, and thermal radiation can't travel through the wool along a straight path. As a result, wearing a wool sweater keeps you from losing heat quickly—you stay warm. Wool has the added benefit of carrying water away from your skin.
Firewalls are just insulating, non-flammable walls that prevent the heat from a fire on one side of a firewall from initiating combustion on the other side. As far as I know, most firewalls are made from masonry block. Ceramics such as stone or cement are already fully oxidized and can't burn. Furthermore, most ceramics are poor conductors of heat and many can become almost white hot without melting. As long as a masonry wall is thick enough and sturdy enough, it can tolerate having a fire on one side without conveying that fire's heat to the combustible materials on its other side. If there aren't any holes or flaws in the firewall, it will prevent the spread of fire between adjacent buildings.
Polyesters are a class of polymers, extremely long molecules that are commonly known as plastics. Each polyester molecule is several thousand atoms long, so that a polyester fiber resembles a tiny rope made of microscopic spaghetti strands that are all entangled with one another. Like most electric insulators, polyester plastic is a poor conductor of heat. But in clothing its main insulating effect is to trap air. While air is a terrible conductor of heat, it tends to undergo convection and convection allows it to transport heat pretty effectively. However, when air is trapped by countless tiny fibers, convection is inhibited and the air becomes a great insulator. That's why polyester fibers are such good thermal insulation—they trap air and let the air act as the real insulation.
Yes, you should be able to make your own thermal windows. The value of having two vertical panes of glass that are separated by a narrow gap is that heat has trouble flowing across gap. While air is a poor conductor of heat, it carries heat reasonably well via convection. But with only a narrow gap of air between two vertical glass panes, convection doesn't work well. Air heated by its contact with the warmer pane tends to flow directly upward, rather than toward the cooler pane. Similarly, air cooled by its contact with the cooler pane tends to flow directly downward, rather than toward the warmer pane.
But as you've anticipated, you may have trouble with condensation on the inside surface of the cooler pan. Your best bet at avoiding this problem is to completely seal the space between the two panes and to fill it with very dry air or even bottled nitrogen gas—which can be obtained cheaply from a local gas supply company. You'd have to blow the dry air or nitrogen in through one hole and allow the trapped air to flow out through another hole. After the trapped air has been replaced several times with dry gas and you're sure there is little moisture left between the panes, you can stop replacing the air and seal both holes. But with stained glass, you have many potential gaps through which moisture can enter the trapped air, so achieving a seal could be very difficult. In that case, you might just put a desiccant at one edge of the window. Drierite is an inexpensive material that resembles little white pebbles and that can absorb quite a bit of moisture. If you put some Drierite between the two panes before you did your best to seal the space between them, I would expect the Drierite to remove enough moisture from the trapped air to avoid condensation problems. After a few years, enough moisture may have leaked in through cracks to cause trouble, in which case you would simply replace the Drierite. One useful type of Drierite is blue when fresh and turns pink when it has absorbed its fill of moisture.
Amazingly enough, air's ability to carry heat doesn't change much as you reduce its pressure and density as long as you stay above about a thousandth of atmospheric pressure and density. That's because reducing the density of air molecules may leave fewer particles to carry heat, but it also allows them to travel farther before they collide with other molecules. The reduction in molecular density is almost perfectly cancelled by an increase in the mean free path those molecules travel between collisions—there are fewer heat carriers, but they can move more easily. It isn't until you reach very low pressures and densities—so that the mean free path begins to approach the size of the enclosed gas—that reducing the air pressure and density begins to decrease the air's ability to carry heat. That's why even a small leakage of gas into a vacuum flask spoils that flask's insulating characteristics. However, you can decrease the "air's" ability to carry heat by increasing the mass of its molecules—heavier particles such as carbon dioxide or krypton travel more slowly than normal air molecules and don't carry heat as well.
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