Search settings per site

That would need to be a small independent module. It should be fairly simple to achieve. In D7 you can use hook_node_grants_alter() to change the grants array. In this case, you would do it IFF the path indicates a search.

Something like:

function custom_node_grants_alter(&$grants, $account, $op) {
  $_domain = domain_get_domain();
  $path = arg(0);
  // If not a search path, do nothing.
  if ($path != 'search' || $op != 'view') {
    return;
  }
  // Check the default domain. If so, grant all. 
  // Note that this syntax only works for 7.x.3, in 7.x.2 use domain_default().
  if ($_domain['is_default'])) {
    $grants = array('domain_all' => array(0));
    return;
  }
  // Otherwise, set our rules.
  $domains = domain_get_domains();
  switch ($_domain['domain_id']) {
    case 2:
       // something;
       break;
  }
}

The fun part would be a module that creates a UI for setting these rules. Sounds like a good project for someone to take on.

I'll close this issue due to inactivity for 14 years and there is upcoming EOL of Drupal 7 in January 2025. While the project's version for Drupal 7 will surely keep providing support for security issues and website breaking bug fixes for Drupal 7, we should try to minimize the open issues for Drupal 7 in the queue as much as possible. A big thanks around for the report and all the efforts in here. Feel free to re-open if you can provide a fix or found an additional related problem which increases the issue priority.