Granting API custom/full access role in Magento 1.6.2 (Web Services > Roles) simply doesn't work.
How to we fix it?

Copy app/code/core/Mage/AdminHtml/Block/Api/Tab/RolesEdit.php

To: app/code/local/Mage/AdminHtml/Block/Api/Tab/RolesEdit.php

Inside, place the following:

class Mage_Adminhtml_Block_Api_Tab_Rolesedit extends Mage_Adminhtml_Block_Widget_Form {

    public function __construct() {
        parent::__construct();

        $rid = Mage::app()->getRequest()->getParam('rid', false);

        $resources = Mage::getModel('api/roles')->getResourcesList();

        $rules_set = Mage::getResourceModel('api/rules_collection')->getByRoles($rid)->load();

        $selrids = array();

        foreach ($rules_set->getItems() as $item) {
			if (array_key_exists(strtolower($item->getResource_id()), $resources)
                           && $item->getApiPermission() == 'allow') {
                $resources[$item->getResource_id()]['checked'] = true;
                array_push($selrids, $item->getResource_id());
            }
        }

        $this->setSelectedResources($selrids);

        $this->setTemplate('api/rolesedit.phtml');
    }
}

Write your own "API":

1. app/code/local/Engineering/Extapi/controllers/ExtapiController.php

<?php

class Engineering_Extapi_ExtapiController extends Mage_Core_Controller_Front_Action
{

	protected function _initAction() {
		return $this;
	}

	public function indexAction() {
		$this->loadLayout();
	}

	public function getnumberofordersAction()
	{
		if($this->getRequest()->getParam('pass')=="123")
		{ //check password
			$query = "SELECT count(*) FROM `sales_flat_order`";

			$resource = Mage::getSingleton('core/resource');
			$readConnection = $resource->getConnection('core_read');
			$result = $readConnection->fetchOne($query);	

			echo $result;
		}
	}

	public function getnumberofcustomersAction() {
		if($this->getRequest()->getParam('pass')=="123")
		{ //check password
			$query = "SELECT count(DISTINCT email) FROM customer_entity";

			$resource = Mage::getSingleton('core/resource');
			$readConnection = $resource->getConnection('core_read');
			$result = $readConnection->fetchOne($query);		

			echo $result;
		}
	}

}

2. app/code/local/Engineering/Extapi/etc/config.xml

<?xml version="1.0"?>
<config>
    <modules>
        <Engineering_Extapi>
            <version>0.1.0</version>
        </Engineering_Extapi>
    </modules>

    <frontend>
        <routers>
			<extapi_router>
				<use>standard</use>
				<args>
					<module>Engineering_Extapi</module>
					<frontName>extapi</frontName> <!-- URI -->
				</args>
			</extapi_router>
        </routers>
    </frontend>
</config>

Now - Don't forget to create the app/etc/modules/Engineering_Extapi.xml file:

<?xml version="1.0"?>
<config>
    <modules>
	    <Engineering_Extapi>
	       <active>true</active>
               <codePool>local</codePool>
	    </Engineering_Extapi>
    </modules>
</config>
Now you can reach the actions via:

http://yoursite.com/extapi/getnumberoforders/?pass=123

http://yoursite.com/extapi/getnumberofcustomers/?pass=123

Sometimes we would like to send a customized transactional email right after a transaction has been made.
How would we do it? Simple. Create an Observer and hook it up with Magento's checkout -success event (checkout_onepage_controller_success_action).

Let's create and extension dir (Transemail) with 2 files in it:

1. app/code/local/Engineering/Transemail/Model/Observer.php:
<?php
class Engineering_Transemail_Model_Observer extends Mage_Core_Model_Abstract {

    public function sendMail($observer)
    {
		$event = $observer->getEvent();
		if(!$order = $event->getOrder())
		{
			$order_Id = Mage::getSingleton('checkout/type_onepage')->getCheckout()
                                  ->getLastOrderId();
			$order = Mage::getModel('sales/order')->load($order_Id);
		}
		$payment = $order->getPayment()->getMethod();

			$loginfos = false;	//shows informations on the progress data
			$addhistoryactive = false; //history and statuschange is saved in orders

			// Transactional Email Template's ID
			$templateId  = 1; //choise template

			// Set sender information
			$senderName = Mage::getStoreConfig('trans_email/ident_support/name');
			$senderEmail = Mage::getStoreConfig('trans_email/ident_support/email');
			$sender = array('name' => $senderName,'email' => $senderEmail);

			// Get Store ID
			$storeid = Mage::app()->getStore()->getId();
			$billing_details = $order->getBillingAddress();
			$payment_data = $order->getData();
			$gender = $payment_data['customer_gender'];//$billing_details->getGender();
			$customer_name = $billing_details->getLastname();

			if($addhistoryactive)
			{
				//add history comment
				$comment = 'blabla';
				$order->addStatusHistoryComment($comment);
				$order->save();
			}

			if($gender==1)
			{ //1-male, Magento standard
				$gender_html = "Mr. ".$customer_name;
			}
			else
			{ //0-female, Magento standard
				$gender_html = "Mrs. ".$customer_name;
			}					

			// Set recepient information
			$recepientEmail = $billing_details->getEmail();
			$recepientName = $billing_details->getFirstname()." "
                       .$billing_details->getLastname();

			$payment = $order->getPayment();
			$method = $payment->getMethodInstance();
			$addinfo = $order->getPayment()->getAdditionalInformation();
			$grandtotal = $order->getGrandTotal();

			$paymentBlock = Mage::helper('payment')->getInfoBlock($order->getPayment())
                       ->setIsSecureMode(true);
                        $paymentBlock->getMethod()->setStore($storeId);
                        $paymentBlockHtml = $paymentBlock->toHtml();
			 // Set variables that can be used in email template
			$vars = array('customerName' => 'test',
					'customerEmail' => $recepientEmail,
					'gender_html' => $gender_html,
					'order' => $order,
					);

			// Send Transactional Email
			$mailTemplate = Mage::getModel('core/email_template');
			$mailTemplate->setTemplateSubject('subject');
			$mailTemplate->setDesignConfig(array('area' => 'frontend'));
			$mailTemplate->sendTransactional($templateId, $sender, $recepientEmail,
                        $recepientName, $vars, $storeId);

        return true;
    }

}

2. app/code/local/Engineering/Transemail/etc/config.xml:
<?xml version="1.0"?>

<config>

<modules>

<Engineering_Transemail>

<version>0.1.0</version>

</Engineering_Transemail>

</modules>

<frontend>

<events>

<checkout_onepage_controller_success_action>

<observers>

<transemail_observer>

<type>singleton</type>

<class>Engineering_Transemail_Model_Observer</class>

<method>sendMail</method>

</transemail_observer>

</observers>

</checkout_onepage_controller_success_action>

</events>

</frontend>

</config>

Now - Don't forget to create the app/etc/modules/Engineering_Transemail.xml file:

<?xml version="1.0"?>
<config>
    <modules>
	    <Engineering_Transemail>
	       <active>true</active>
               <codePool>local</codePool>
	    </Engineering_Transemail>
    </modules>
</config>