Magento – How to add products in cart and wishlist with external code outside Magento

You can add a product via POST to checkout/cart/add/product/<id> and add more simple items via $_GET['related_products'] = array('id', 'id2', ...)

This happens because the configurable product does not have minimum sale qty and a total qty.
You need to get the simple product that is represented by the configurable product and get the values from it. Try this:

$simpleProduct = null;
foreach ($_item->getQuote()->getAllItems() as $simpleItem){
   if ($simpleItem->getParentId() == $_item->getId()){
       $simpleProduct = $simpleItem->getProduct();
       break;
   }
}
if ($simpleProduct){
   //work your magic with $simpleProduct
}

I didn't test, but it seams like the way to go.
I've tested and this works for me. I was close. Instead of getParentId() it should be getParentItemId(). Here is the code from my checkout/cart/item/default.phtml file:

$simpleProduct = $this->getProduct();
if ($this->getProduct()->getTypeId() == 'configurable') {
    foreach ($_item->getQuote()->getAllItems() as $simpleItem){
        if ($simpleItem->getParentItemId() == $_item->getId()){
            $simpleProduct = $simpleItem->getProduct();
            break;
        }
    }
}
$stockItem = Mage::getModel('cataloginventory/stock_item')->loadByProduct($simpleProduct);
$min_sale_qty = (int)$stockItem->getData('min_sale_qty');
$total_qyt = (int)$stockItem->getQty();

?>
<select name="cart[<?php echo $_item->getId() ?>][qty]">
    <?php for($i = $min_sale_qty; $i <= $total_qyt; $i = $i + $min_sale_qty) : ?>
        <option value="<?php echo $i?>" <?php echo ($i == $this->getQty())? "selected=selected": ""; ?>>
            <?php echo $i?>
        </option>
    <?php endfor;?>
</select>

I'm almost sure that there is an other way of getting the simple product and avoid the foreach loop but this will do for now.