Add product to cart

$product = Mage::getModel('catalog/product')->load(87);  // Random product ID

// get cart and add product
$cart = Mage::getSingleton('checkout/cart'); 
$cart->init();
$cart->addProduct($product, 2);

// update session
$session->setCartWasUpdated(true);

// save the cart
$cart->save(); 

Customer Login

Customer Login:
	    umask(0);
	    ob_start();
	    session_start();
	    Mage::app('default');
	    $websiteId = Mage::app()->getWebsite()->getId();
            $store = Mage::app()->getStore();
	    $customer = Mage::getModel("customer/customer");
	    $customer->website_id = $websiteId;
	    $customer->setStore($store);
            $customerEmail = "example@gmail.com";
            $customer = Mage::getModel('customer/customer')->setWebsiteId($websiteId)->loadByEmail($customerEmail);
	    try {
                 $customer->loadByEmail("example@gmail.com");
                 $session = Mage::getSingleton('customer/session')->setCustomerAsLoggedIn($customer);
                 $a = $session->login($customerEmail, "Magentodf3d");
                 if(Mage::getSingleton('customer/session')->isLoggedIn()):
                 $customer = Mage::getSingleton('customer/session')->getCustomer()->getName();
                 $customer = Mage::getSingleton('customer/session')->getCustomer();
                 Mage::getSingleton("core/session", array("Name" => "frontend"));
                 $session=Mage::getSingleton('customer/session', array('Name'=>'frontend') );
        
	                if ( $session->isLoggedIn() ) {
	                        $session = Mage::getSingleton('customer/session')->setCustomerAsLoggedOut($customer);
	                        // $session->logout();
	                        if ( $session->isLoggedIn() ) {
		                      echo "secondlogged in";
	                        }else{
		                      echo "not secondlogged in";
	                        }
		        } else {
			        echo "not logged in";
		        }

                        endif;

                }
            catch(Exception $e){

		}

Get All store Details

$allStores = Mage::app()->getStores();
foreach ($allStores as $_eachStoreId => $val) 
{
$_storeCode = Mage::app()->getStore($_eachStoreId)->getCode();
$_storeName = Mage::app()->getStore($_eachStoreId)->getName();
$_storeId = Mage::app()->getStore($_eachStoreId)->getId();
}

Remove Product from Magento Cart

$id = '87'; // replace product id with your id
$cartHelper = Mage::helper('checkout/cart');
$items = $cartHelper->getCart()->getItems();
foreach($items as $item):
if($item->getProduct()->getId() == $id):
$itemId = $item->getItemId();
$cartHelper->getCart()->removeItem($itemId)->save();
break;
endif;
endforeach; 

Upadate product price:

Mage::app('admin')->setCurrentStore(1);
// Mage::app()->setCurrentStore($store_id);
// Mage::run($mageRunCode, $mageRunType);

$store = Mage::getModel('core/store')->load(1);
echo $store->getCode();
// $store = Mage::app()->getStore();
// echo $store;
Mage::getSingleton('core/session', array('name'=>'frontend'));
$_product = Mage::getModel('catalog/product')->load(87); /*87 is Product ID
$_product->getPrice();
echo $_product->getPrice();
$_product->setPrice(400);
$_product->save();
echo $_product->getPrice();