How to alter the Views UI config form Part 1: How do I add a form element (ie checkbox) to the field of a specific type (ie all image fields) inside the admin Views UI.  What code do I need include in a custom module.  

Part 2: How do I save it to the database.



This is not a default view.
I am not creating a need field.  I am trying to alter an existing field.
You need to use Views handlers https://api.drupal.org/api/views/views.api.php/group/views_handlers/7.

Basically, you need to extend the handler class that is used by that field which in your case is field_image. 

In order to start and make your custom handler work you need two basic functions to tell Views you mean some business with them. These are  hook_views_api() and hook_views_data_alter() function.

MODULE.module

/**
 * Implements hook_views_api().
 */
function uc_addons_views_api() {
  return array(
    'api' =&gt; 3,
    'path' =&gt; drupal_get_path('module', 'uc_addons') . '/views',
  );
}


MODULE.views.inc

/**
 * Implements hook_views_data_alter().
 */
function uc_addons_views_data_alter(&amp;$data) {
  dsm($data);
}


The hook_views_data_alter() function needs to be inside your MODULE.views.inc file.

Lastly of course is your handler w/c adds your field by extending the base handler as you can get more idea from the link. Also from my experience, the saving of values from fields are taken care by Views already.