Wei-ling: That's a nice set of closely related questions. I'll try to give a first answer, but it won't be very deep. We'd welcome follow-up questions.
Most of the questions you asked deal with something called surface tension. There are several ways to try to picture this effect. Water molecules are naturally electrically polarized and stick well to each other. The ones on the surface with air are missing some of the molecules that they would stick to if they were in the middle of the liquid. They have higher energy than the other molecules. Things tend to pull toward states of lower energy (that's why things fall, springs push or pull to their low energy lengths, etc.) So the liquid pulls into shape to reduce the number of molecules on the bare surface.
a. Since the raindrops are surrounded by bare surface, they form the shape which has the least surface for a given volume of water. That's the sphere.
b. A needle will sink once it gets under the surface. But to break through the surface first requires pushing some water molecules apart, raising their energy. Unless something jostles the needle, that doesn't happen.
e. Same for insect as for needle.
c. Adding detergent lowers the surface tension. That's because detergent molecules have one end that sticks well to water and another that doesn't. The ends that don't stick well to water coat the needle (or piece of dirt, etc) leaving the other ends in the water. So the needle can now slide into the water without making water molecules lose their bonds with something to which they stick well.
d. The hairs really each stick to the water. Pulling them apart would increase the surface of bare water, increasing the energy.
f. Towels have lots of little fibers which stick well to water. Polyethylene sheets have much less surface and don't stick so well to water to begin with. Most plastics are made from polymers which share similarities with oil (and in fact petroleum is used to manufacture most plastics). Water molecules prefer to stick to other water molecules than to oil molecules.
g. I don't know much about paint. You're getting at the general question of how some things (water with water) stick well and others (water with teflon) don't. Some paints are oil-based to make this question even more complicated.
One of the main reasons is often something called hydrogen bonds. Water has two hydrogen atoms per molecule. They are somewhat positively charged, electrically, so they tend to stick to negative charges, like the oxygen atom on another water molecule. Another important ingredient is that the atoms in a water molecule don't line up in a straight line like this: H-O-H. Instead, there is a bend in the water molecule, so the hydrogen atoms stick out on one side and the oxygen sticks out back the other way.
If there are many slightly negatively charged sites on a typical wall, water-based paints would form a lot of hydrogen bonds with them. A wall made of teflon would not work.
Some walls (like wood or plaster) are porous -- they have lots of tiny little holes in them. If the water makes hydrogen bonds with the molecules on the surface of the wall, the energy is lower for more water molecules to make more bonds. Since water sticks to itself, more water is dragged into the holes as molecules in front seek to lower their energies by making more hydrogen bonds with the surface of the wall. This is called "capillary action" and is also responsible for water lifting in tree trunks. The whole business of what kinds of substances will make others "wet" is rather involved and much effort is spent understanding it because of its practical significance. We often try to make substances wet others more easily (as in paint, glues, soap, shampoo, lubricating oil, solder flux) or less easily (car wax, house siding, waterproof clothing, food packaging).
Mike W. (and Tom)
(republished on 08/01/06)