Where is the documentation for core associative arrays?
Render arrays are defined (in Drupal 7) with the hook_element_info hook.

To see what attributes a render element can accept you can check the MODULE_element_info function that defined it.

For example looking at system_element_info we can see that the page render element accepts a #show_messages attribute and that it contains a boolean value.

For more information you can also look for the template_preprocess_ELEMENT function for the element.

template_preprocess_page in our example.