How to change end date automatically after changing start date?
I did it the way pretty much mentioned in question with some corrections.

My code with javascript file is 

// Change the end date value to same as that of start date.
Drupal.behaviors.form_modif = {
  attach: function (context, settings) {
        $('input#edit-field-event-date-und-0-value-datepicker-popup-0').change(function(){
        var field_date1 = $('input#edit-field-event-date-und-0-value-datepicker-popup-0').val(); 
        $('input#edit-field-event-date-und-0-value2-datepicker-popup-0').val(field_date1);
    });
  }
};


}(jQuery));