Form loaded with ajax call not having autocomplete enabled
If you want Drupal's autocomplete, you need to modify form using Form API '#ajax'. If you are doing it with your custom scripts, Form API will not know that field really belongs to your form, and will not handle field's calls.1

The way you should do it is:


In your form building function, create element with '#ajax' property, that will be responsible for loading your form part, or add it to existing element.
Also in your form building function, add an if that will check triggering element ($form_state['triggering_element']), and if that was your button, add entry in $form_state that new section should be visible.
If there is an entry mentioned in 2., output form part you want to be loaded with AJAX.
Use AJAX callback function only to select and return proper part of the form.




1 Simplified explanation, of course.