Some serious errors

Hi,

I don't understand your problems.
Your cart is working properly. I didn't had any problems adding/removing products from it.

You don't have the "payment" view in your checkout workflow. So there is no payment.
What is the problem with the shipping method ?

If you want another message at the end of the checkout, you can edit the file "end" of the view "checkout" via the menu Display->Views.
There you can add the order number and the price of the order like that:
$app =& JFactory::getApplication();
$order_id = $app->getUserState( HIKASHOP_COMPONENT.'.shipping_id' );
$orderClass = hikashop_get('class.order');
$order = $orderClass->loadFullOrder($order_id);

echo $order->order_number;

echo $order->order_full_price;

1. Do you have some kind of error in that case ? What happens ? I didn't see any problem.

2. When you login the display of the page change since the registration form is removed. So the system stays on the same page.
You are registering, not finishing the order.
If you don't want to have it twice, change your checkout workflow to have three steps:
cart then login then shipping

3. Ah yes, try with that code instead:
$app =& JFactory::getApplication();
$order_id = $app->getUserState( HIKASHOP_COMPONENT.'.shipping_id' );
$orderClass = hikashop_get('class.order');
$order = $orderClass->loadFullOrder($order_id,false, false);

echo $order->order_number;

echo $order->order_full_price;