Magento 1.9 – Rate Table Shipping Showing $0.00 for Certain Products

You can do the same without a rewrite using an observer:

<sales_quote_collect_totals_before>
    <observers>
        <your_module>
            <type>singleton</type>
            <class>your_module/observer</class>
            <method>salesQuoteCollectTotalsBefore</method>
        </your_module>
    </observers>
</sales_quote_collect_totals_before>

Then, in the observer:

public function salesQuoteCollectTotalsBefore(Varien_Event_Observer $observer)
{
    /** @var Mage_Sales_Model_Quote $quote */
    $quote = $observer->getQuote();

    $store = Mage::app()->getStore($quote->getStoreId());
    $store->setConfig('carriers/tablerate/name', 'Name By Country');
    $store->setConfig('carriers/tablerate/title', 'Method Title By Country');
}

Setting the config values dynamically without saving them is a cheap trick but it works pretty well.
The benefit of using an observer over a class rewrite is that it's less conflict prone.

If after uploading the file and after clicking on "save config", you are getting this "no file selected" then it is totally alright your file is uploaded. Above, on the same page you can see notice something "The configuration has been saved."