The USGS supports an important National Earthquake Hazards Program. As a small part of that effort there have been studies attempting to correlate magnetic variations, or more precisely, electro-magnetic variations, with earthquakes.
Yes. We know this from an examination of the geological record.
One of the most important jobs that a scientist has is to identify -- from among all the possible causes and effects in nature -- those that are the most important and strictly and necessarily causally related, and those that are simply insignificant a
The magnetic field of the Earth does protect us from fast-moving charged particles streaming from the Sun, and so does the atmosphere.
The needle of a compass is a small magnet that is allowed to pivot in the horizontal plane. The needle experiences a torque from the ambient magnetic field of the Earth.
Fields fill the space between matter and they determine how it is that bits of matter can exert forces on other bits of matter at a distance. 
Briefly, as the result of radioactive heating and chemical differentiation, the Earth's outer core is in a state of turbulent convection.
Almost certainly not. Direct historical measurements of the intensity of the geomagnetic field have been possible ever since Gauss invented the magnetometer in the 1830's.