Use core code of QGIS in my own Python scripts

I would like to know if I can use the code of the default functions that come in QGIS, for example the Intersection function.

When you click on the help button it redirects you to the user guide where comes de description of the function and there is a section "Python code" where comes a small code for that specific function.
In almost all the vectors geoprocessing the library "processing" appears. But I could not install it from anywhere.

Does anyone know if it is possible use this code and library in my own Python script?