. Is the earth a huge magnet? If so, how does it do this without being made out of metal?
The earth is a huge magnet and it is made out of metal. The earth's core is mostly iron and nickel, both of which can be magnetic metals. However, the earth's magnetism doesn't appear to come from the metal itself. Current theories attribute the earth's magnetism to movements in and around the core. There are either electric currents associated with this movement or some effects that orient the local magnetization of the metal. I don't think that there is any general consensus on the matter.
. What keeps the earth stable so that it doesn't get pulled up into the "magnet"?
If you are asking why doesn't the earth itself get pulled up toward a large magnet or electromagnet that I'm holding in my hand, the answer is that the magnetic forces just aren't strong enough to pull the magnet and earth together. I'm holding the two apart with other forces and preventing them from pulling together. The forces between poles diminish with distance. Those forces are proportional to the inverse square of the distance between poles, so they fall off very quickly as the poles move apart. Moreover, each north pole is connected to a south pole on the same magnet, so the attraction between opposite poles on two separate magnets is mitigated by the repulsions of the other poles on those same magnets. As a result, the forces between two bar magnets fall over even faster than the simple inverse square law predicts. It would take an incredible magnet, something like a spinning neutron star, to exert magnet forces strong enough to damage the earth. But then a neutron star would exert gravitational forces that would damage the earth, too, so you'd hardly notice the magnetic effects.
. How do the sizes of two magnets determine how much paper can be held between them? — D
While the full answer to this question is complicated, the most important issues are the strengths and locations of the magnetic poles in each magnet. Since each magnet has north poles and south poles of equal strengths, there are always attractive and repulsive forces at work between a pair of magnets—their opposite poles always attract and their like poles always repel. You can make two magnets attract one another by turning them so that their opposite poles are closer together than their like poles (e.g. by turning a north pole toward a south pole).
To maximize the attraction between the magnets, opposite magnetic poles should be as near together as possible while like magnetic poles are as far apart as possible. With long bar magnets, you align the magnets head to toe so that you have the north pole of one magnet opposite the south pole of the other magnet and vice versa. But long magnets also tend to have weaker poles than short stubby magnets because it takes energy to separate a magnet's north pole from its south pole. With short stubby magnets, the best you can do is to bring the north pole of one magnet close to the south pole of the other magnet while leaving their other poles pointing away from one another. Horseshoe magnets combine some of the best of both magnets—they can have the strong poles of short stubby magnets with more distance separating those poles.
Returning to the paper question, size is less important than pole strength and separation. The stronger the magnets and the farther apart their poles, the more paper you can hold between them.
. I am currently working on a physics project, the magnetic levitation train. How can I make this train move on the track without it crashing? I only have a few days to make it work so I can present it in the science fair. - VC
I'm afraid that you're facing a difficult problem. Magnetic levitation involving permanent magnets is inherently and unavoidably unstable for fundamental reasons. One permanent magnet suspended above another permanent magnet will always crash. That's why all practical maglev trains use either electromagnets with feedback circuitry (magnets that can be changed electronically to correct for their tendencies to crash) or magnetoelectrodynamic levitation (induced magnetism in a conducting track, created by a very fast moving (>100 mph) magnetized train). There are no simple fixes if what you have built so far is based on permanent magnets alone. Unfortunately, you have chosen a very challenging science fair project.