Magnetic static fields can pass through Faraday cages. Changing magnetic fields - and the electric fields that they generate - do not, because they induce currents in the Faraday cages.

Wood, being not an electrical conductor, isn't going to do much of anything to a magnetic field, however, although wood waterlogged with seawater will act like a Faraday cage, since seawater conducts electricity. However, dry wood would have very little effect on the magnetic field and yes, you could levitate it if there were current flowing through it.

I agree with everyone. I did an experiment with a magnet, a paper clip, and a toothpick. With the magnet and the paper clip lying on a table, the magnet could pull the paper clip when they were about the width of the toothpick apart. When I put the toothpick between the magnet and the paper clip, the magnet could still pull the paper clip.

Here are more answers. "Materials that are not attracted to a magnet like air, wood, plastic, brass, etc., have a permeability of, essentially, 1. There is no magnetism induced in them by an external magnetic field, and therefore, they are not attracted by a magnet."

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