How do I check the access to every node?
There are several ways to do alter or hook into node access. You can find out more by reading the Node Access Rights page on api.drupal.org.

Briefly node access works like this (paraphrasing from the aforementioned documentation page):


Users with 'bypass node access' are granted access.
Invoke implementations of hook_node_access
Invoke implementations of hook_node_grants


Finally,


  To see how to write a node access module of your own, see node_access_example.module.