That is actually a very 'modern' question, because scientists are still debating that. Some scientists in France say that their measurements say that the magnetic field does affect gravity. By how much? Well, it depends on where you are on earth. We know that the magnetic field is stronger near the poles and weaker near the equator, and some scientists have calculated that gravity does differ from place to place. However, we still don't have experimental evidence from this and many scientists are not convinced that they do affect each other. Maybe someday we'll find out.

Great question! The short answer is no. Gravity is a field caused by the mass of the center of the earth. It draws objects to the center of the earth (which when we drop something, the center of the earth appears as "down").

The magnetic field is a separate thing affecting the earth. It causes the needle on our compasses to point to north, it causes the northern lights, and it allows geese to fly south for the winter. For the most part they are very separate fields.

Magnetic fields contain energy, and energy can exert a gravitational field. Aside from that, no, gravity and magnetism are different forces.