Remove tabledrag statuses on Ajax submit and display status message after Ajax submit
I managed to solve this finally. My answer to both questions was Ajax Commands. 

To anyone looking for the solution, here's what I did:

Question 1:

Instead of messing around with Dragtable, it's easier to just re-create the form and pass it back so it replaces the original form. I had to rebuild the form in my ajax callback function, then return it with an ajax command. To rebuild the form, you needed to create a new form_state variable and use drupal_rebuild_form function like so:

function my_ajax_form_callback($form, &amp;$form_state) {
  $new_state = array();
  $new_state['build_info'] = $form_state['build_info'];
  $new_state['rebuild'] = TRUE;
  $new_state['values'] = array();
  $new_state += form_state_defaults();

  $new_form_array = drupal_rebuild_form('my_ajax_form_id', $new_state);
  $new_form = drupal_render($new_form_array);

  $commands = array();
  $commands[] = ajax_command_html('#form-container-element-id', $new_form);

  return array('#type' =&gt; 'ajax', '#commands' =&gt; $commands);
}


The original form button that submits to this callback also should have the form-container-element-id in the wrapper element of the #ajax array (it should always be a CSS ID so it shouldn't have the # to indicate it's an ID):

$form['submit'] = array(
  '#type' =&gt; 'submit',
  '#value' =&gt; 'Submit',
  '#ajax' =&gt; array(
    'callback' =&gt; 'my_ajax_form_callback',
    'wrapper' =&gt; 'form-container-element-id',
    'method' =&gt; 'html',
    'event' =&gt; 'click',
  ),
);


Here's the API documentation link for ajax commands: Ajax framework commands (Drupal 7)

Question 2:

The best way to display status messages after an ajax callback is to use theme_status_messages() function. The snippet below also goes in the my_ajax_form_callback function before returning from the function:

drupal_set_message('This is a status message', 'status', FALSE);
$messages = theme_status_messages(array('display' =&gt; 'status'));
$commands[] = ajax_command_html('#status-message-container', $messages);