Is there any code with which I could fetch items added to the shopping cart and their count from Magento using any models or helpers?
To get your cart object (in session) :
$quote = Mage::getSingleton('checkout/session')->getQuote();
Then, to get the list of items in the cart :
$cartItems = $quote->getAllVisibleItems();
Then, to get the count for each item :
foreach ($cartItems as $item) {
echo $item->getQty();
}