How to move my site files outside the Drupal folder on local computer?
Yes you can separate files folder out of Drupal core installation. 
Follow these steps: 


Go to admin/config/media/file-system
See public file system path, this needs to be relative to drupal installation. So if I want to make the files folder in parent folder of Drupal core installation, I need to give path like ../test_files 
Go to admin/config/development/performance
Clear cache and if you have aggregated css and Js, disable them, clear cache and again enable them. 


This works