How to get nodes from Google Search?
What you're describing is a content recommendation system. This isn't what Google CSE is built for and implementing the way you describe would likely result in poor results. 

You're better off implementing one of Drupal's existing recommendation modules or some other 3rd party recommendation service (e.g. OutBrain).

Some of Drupal's recommendation modules include:


Recommender API: Broad API that ties into other Drupal entities. 
Similar By Terms: Use similar taxonomy terms to find related content.   
Similar Entries: Uses MySQL full text searching to find related content.