Suppose you want to check for earthquake danger before buying a new home. how can you check the regional geology for earthquake danger? the actual building site? the home itself?

In order to check the regional geology for earthquake danger one should view fault and hazard maps of the area. A fault map shows the distribution of faults or fault zones in an area. A fault is a crack in the earth's surface along which movement occurs.

Hazard maps take into consideration the historic occurrences of earthquakes in the region and shows the probability of likely earthquakes in the region.
the actual building site can be assessed by using a soils map. Different soils react in different ways to seismic waves. The amplitude of seismic waves are either amplified or suppressed depending on the
type of soil or bedrock.
Homes showing signs of susceptibility to earthquakes often have cracks in the structure. These can be caused by minor quakes.

That is true it is called an aftershock