Dynamically Get Zip Code on Shipping Form – Magento 1.9

It seems you want to calculate shipping cost for individual product and not on for whole cart total. In that case you follow below code to calculate shipping cost per product:

<?php
class Yanted_Export_Helper_Shipping extends Mage_Core_Helper_Abstract
{
    public function calculateShippingCosts($productId, $country,$zipcode, $storeId = 1)
    {
        $product = Mage::getModel('catalog/product')->load($productId);
        $item = Mage::getModel('sales/quote_item')->setProduct($product)->setQty(1);
        $store = Mage::getModel('core/store')->load($storeId);

        $request = Mage::getModel('shipping/rate_request')
            ->setAllItems(array($item))
            ->setDestCountryId($country)
            ->setPackageValue($product->getFinalPrice())
            ->setOrigPostcode($zipcode)  
            ->setPackageValueWithDiscount($product->getFinalPrice())
            ->setPackageWeight($product->getWeight())
            ->setPackageQty(1)
            ->setPackagePhysicalValue($product->getFinalPrice())
            ->setFreeMethodWeight(0)
            ->setStoreId($store->getId())
            ->setWebsiteId($store->getWebsiteId())
            ->setFreeShipping(0)
            ->setBaseCurrency($store->getBaseCurrency())
            ->setBaseSubtotalInclTax($product->getFinalPrice());

        $model = Mage::getModel('shipping/shipping')->collectRates($request);
        $costs = array();

        foreach($model->getResult()->getAllRates() as $rate) {
            $costs[$rate->getCarrier()] = array(
                'title' => trim($rate->getCarrierTitle()),
                'price' => $rate->getPrice()
            );
        }

        return $costs;
    }
}

You need to create your action and should make an ajax call to get this rate dynamically.

<?php
$costs = Mage::helper('yanted_export/shipping')->calculateShippingCosts('123', 'US','10007', 2); 

Hope this can resolve your problem.

you don't need to add an observer for that.
For system->config values you can use a backend model.
In system.xml where you declare your field do this:

<field_name_here translate="label">
    <label>Label here</label>
    <frontend_type>text</frontend_type>
    <backend_model>[module]/something_here</backend_model><!-- add this one -->
    <sort_order>10</sort_order>
    <show_in_default>1</show_in_default>
    <show_in_website>1</show_in_website>
    <show_in_store>1</show_in_store>
</field_name_here>

Then you create the model [Namespace]_[Module]_Model_Something_Here

<?php 
class [Namespace]_[Module]_Model_Something_Here extends Mage_Core_Model_Config_Data
{
    protected function _beforeSave()
    {   
        //get the value being saved
        $value = $this->getValue();
        $isValid = your custom validation here
        if (!$isValid) {
            Mage::throwException(
                Mage::helper('[module]')->__('your error message here')
            );
        }

    }
}

This will prevent the value from saving in case it is wrong and you will see an error message at the top of the page.
You can see a working example for the field base_url from app/code/core/Mage/Core/etc/system.xml that uses the backend model adminhtml/system_config_backend_baseurl which translates to the class Mage_Adminhtml_Model_System_Config_Backend_Baseurl