Can't correctly reference bundle in EntityFieldQuery, field_get_items
A couple of things...first one is you haven't loaded the nodes. If you change

$stories = $result['node'];


to

$stories = node_load_multiple(array_keys($result['node']));


You'll have the fully loaded node objects available.

The other two things are both related; field_view_field() and field_view_value() both accept a single entity; currently you're trying to pass an array, which it won't like.

A simple loop will fix that:

foreach ($stories as $story) {
  $output[] = field_view_field('node', $story, 'field_date');
}


And similar for field_get_items().