How can I change the Magento order’s status to processing
You need to load Magento order object by order id, then set status of the order to be processing
$orderNum = 1;
$order = Mage::getModel('sales/order')->loadByIncrementId($orderNum );
$order->setState(Mage_Sales_Model_Order::STATE_PROCESSING)
->setStatus(Mage_Sales_Model_Order::STATE_PROCESSING)
->save();