A symbolic representation of the earth's surface or part of the earth surface is called map.
A map.
The two dimensional representation of the Earth's surface on piece of paper is called a map. Maps can show an area in great detail or in very broad outlines.
a map
A map is not a three dimensional representation of earth's surface. The best three dimensional representation of earth's surface is a globe or a topographical map.
Assuming you are referring to a representation of the earth then it would be a map.
Height above earths surface is called elevation
Subsidence.
It is called the crust.
Projection
Magma once it reaches the earths surface is called lava.
There is no such thing as half of the Earth. If you are referring to half of the spherical shape of the Earth then it will be a hemisphere.
That would be called fog.