Your knowledge of magnetism is lacking. Iron does not have a polarity, it is simply attracted to any magnetic field. The Earth's magnetic field is very weak, about 2.5 × 10^-05 teslas on average. In comparison, a refridgerator magnet has 1/10 of a Tesla. You expect a magnetic field several times weaker than a refridgerator magnet to make birds fly off into space?
Like I said, magnetic field strength of the magnetosphere is really tiny, and it drops off the farther a way you go by a factor of 1/r^2, where r is the distance. The moon is about 400,000 km away, the magnetic field due to the Earth on the moon is neglibile.
I have a question, though. If it's not repolarizing for 200,000 years, how come we still have it? I mean, it's caused by the hot insides of Earth. However, you fail to understand, too, that magnets LOSE strength over time. 20,000 years ago, the Earth would have been destroyed by the heat of the planet.