how to display order number and shipment method

You should already have the line:
echo JText::sprintf('ORDER_CREATION_SUCCESS_ON_WEBSITE_AT_DATE',$url,HIKASHOP_LIVE, hikashop::getDate(time(),'%d %B %Y'), hikashop::getDate(time(),'%H:%M'));?>

in your order creation email which displays the order number in the $url parameter.

For the shipping method, you could try something like this:

$pluginsShipping = hikashop::get('type.plugins');
$pluginsShipping->type='shipping';
$pluginsShipping->order=$data;
$shipping_method = $pluginsShipping->getName($data->order_shipping_method,$data->order_shipping_id);
echo '<tr><td colspan="4" style="text-align:right">'.JText::_('HIKASHOP_SHIPPING_METHOD').' : '.$shipping_method.'</td></tr>';

For the customer account, you would have to replace that line by:
<div class="header hikashop_header_title"><h1><?php $user =& JFactory::getUser(); echo JText::_('CUSTOMER_ACCOUNT'). ' '.$user->get('name');?></h1></div>