All content types displaying in "Show only items where" search
Yes. You can alter the form's select box with a hook_form_alter() invocation. All that's needed is to remove the options that aren't relevant to the user. 

For example, if you wanted to remove content types where the user didn't have the Edit any TYPE content or Edit all TYPE content permissions, you could do the following:

function token_form_node_admin_content_alter(&amp;$form, $form_state, $form_id) {
  global $user;
  $types = &amp;$form['filter']['filters']['status']['filters']['type']['#options'];
  foreach($types as $type =&gt; $type_name) {
    if($type != '[any]' &amp;&amp; 
       (!user_access("edit any $type content", $user) &amp;&amp; 
        !user_access("edit own $type content", $user))) {
      unset($types[$type]);
    }
  }
}