Mix shader node and add shader nodes combine shaders using different approaches. If I remember correctly add shader node is more for volume materials. I could be wrong on that. The mix shader node is used to combine two shaders. The fac determine the mix amount. You can use an image texture to have different mix amounts across the surface of the object.
For mapping: Blender by default uses UV Map coordinates. If there isn’t a UV Map then it uses Generate. You can define the coordinate by using Texture coordinate node(Shift+a->Input). The Mapping node that you show is used to adjust or change the starting point of the coordinates. The Normal Map node is used to convert a normal map texture to face normal data. It is used to create the illusion that the mesh has more geometry than it does. For example: Instead of modeling a scar on a characters face you can use a normal map to create the illusion that the scar is modeled on the characters face.
