How can a built "map" (128 * 128) be saved and loaded in Minecraft (Vanilla)?
You can copy your worlds. For this you have to open the% appdata% folder, then you take the path as follows: .minecraft> Saves> then just select world and copy. You can then drag them wherever you want.
How can I then load them into a world?
That doesn't work in this case. You can use the mod / plugin Worldeditor to copy areas