Is it possible to have multiple instances of the same field in one content type? I understand that it is best reuse fields where possible and to avoid unnecessary duplication. 

So is it possible to duplicate or reuse a field (or field instance) on the same content type?

For Example: A news article with both a cover image and an image gallery. Is it possible for both to use field_image or must there be two distinct fields, such as field_cover_image and field_gallery_image ???
No, field instance is unique within a content type. See field_create_instance. Relevant code for checking uniqueness in that function:

// Ensure the field instance is unique within the bundle.
// We only check for instances of active fields, since adding an instance of
// a disabled field is not supported.
$prior_instance = field_read_instance($instance['entity_type'], $instance['field_name'], $instance['bundle']);
if (!empty($prior_instance)) {
  $message = t('Attempt to create an instance of field @field_name on bundle @bundle that already has an instance of that field.', array('@field_name' =&gt; $instance['field_name'], '@bundle' =&gt; $instance['bundle']));
  throw new FieldException($message);
}