Magento – What could cause random products to be removed from their categories

Your htaccess is kinda hard to read but nothing seems to redirect the user, I think it's your Magento baseurl that does that.

Have you tried adding the following code to the htaccess to redirect to www. on that level?

RewriteCond %{HTTP_HOST} !^$
RewriteCond %{HTTP_HOST} !^www\. [NC]
RewriteCond %{HTTPS}s ^on(s)|
RewriteRule ^ http%1://www.%{HTTP_HOST}%{REQUEST_URI} [R=301,L]

You cannot sort the products by position field.
This field has meaning only in relation with a category. There is no position attribute for the product (unless you added one by yourself).
You can get all the data you need with one (not so simple) single select. Here goes:

$res = Mage::getSingleton('core/resource');
$eav = Mage::getModel('eav/config');
$nameattr = $eav->getAttribute('catalog_category', 'name');
$nametable = $res->getTableName('catalog/category') . '_' . $nameattr->getBackendType();
$nameattrid = $nameattr->getAttributeId();
//you could add here to select only the attributes you need but I'm lazy and I added all of them (*)
$collection = Mage::getModel('catalog/product')
            ->getCollection()->addAttributeToSelect('*');
$collection->joinTable('catalog/category_product',
    'product_id=entity_id', array('single_category_id' => 'category_id', 'position_in_category'=>'position'),
    null, 'left');
$collection->joinTable(
    $nametable,
    'entity_id=single_category_id',
    array('single_category_name' => 'value'),
    "attribute_id=$nameattrid",
    'left'
);
$collection->groupByAttribute('entity_id');
$collection->getSelect()
    ->columns(array('category_ids_values' => new Zend_Db_Expr("IFNULL(GROUP_CONCAT(`catalog_category_product`.`category_id` SEPARATOR ','), '')")))
    ->columns(array('position_values' => new Zend_Db_Expr("IFNULL(GROUP_CONCAT(`catalog_category_product`.`position` SEPARATOR ','), '')")))
    ->columns(array('category_names' => new Zend_Db_Expr("IFNULL(GROUP_CONCAT(`{$nametable}`.`value` SEPARATOR ','), '')")));

echo $collection->getSelect();

$final['prodCat_list'] = array();
$i = 0;
foreach ($collection as $product){
    $item = array();
    $item['sku']= $product->getSku();
    $item['product_id']= $product->getId();
    $item['name']= $product->getName();
    $item['image']=$product->getThumbnailUrl();
    $item['description']=$product->getDescription();
    $item['short_description']=$product->getShortDescription();
    $item['weight']=$product->getWeight();
    $item['created_at']=$product->getCreatedAt();
    $item['updated_at']=$product->getUpdatedAt();
    $item['price']=$product->getPrice();
    $item['special_price']=$product->getSpecialPrice();
    $item['tax_class_id']=$product->getTaxClassId();
    //this can be retrieved directly with $product->getCategoryIds, but they might be in a different order.
    $item['cat_id'] = $product->getCategoryIdsValues();
    $item['positions'] = $product->getPositionValues();
    $item['category_names'] = $product->getCategoryNames();

    $final['prodCat_list'][] = $item;
}

This code returns and array with product data. An element looks something like this:

       [5] => Array
            (
                [sku] => MA464LL/A
                [product_id] => 25
                [name] => Product name here
                [image] => image/link here
                [description] => Description here.
                [short_description] => Short description here
                [weight] => 10.6000
                [created_at] => 2007-08-24 14:28:50
                [updated_at] => 2008-07-28 21:27:34
                [price] => 2299.9900
                [special_price] => 
                [tax_class_id] => 2
                [cat_id] => 15,28
                [positions] => 0,0
                [category_names] => Computers,Laptops
            )