I'll give it a shot. Let's take them one at a time:

Method 1

$converter=Mage::getModel('sales/convert_order');
$shipment=$converter->toShipment($order);

$converter above is loaded from the class Mage_Sales_Model_Convert_Order, which uses a core helper called copyFieldset to copy order details into a shipment object. $order has to be of type array or Varien_Object.

This method is actually at the core of Method 3, as it uses Mage::getModel('sales/convert_order') in its constructor call.

Key differentiator of this method - it can take an array or an object $order and generate a basic $shipment object. It is a lower-level method used exclusively by the methods you put forth in Method 2, Method 3.

Method 2

 $shipment = Mage::getModel('sales/service_order', $order)
                            ->prepareShipment($this->_getItemQtys($order));

This seems to be the most popular way in Magento's Core of generating a shipment as it is used in both Shipment and Invoice controllers. $order is used as a constructor argument to the instantiation of Mage_Sales_Model_Service_Order, setting it as a protected property on the object.

You're then calling prepareShipment and passing a quantity. As this method uses the converter class from Method 1, you needn't specify more details such as order items pass item shipment qty details in the prepareShipment argument, called here with $this->_getItemQtys. To use this on your own context, all you need to do is pass the quantity of items in an array with the following format:

array(
  'order_item_id'=>$qty,
  'order_item_id'=>$qty,
  'order_item_id'=>$qty
)

Key differentiator of this method - it gives you back a $shipment object, but with all items converted on it. It's plug-and-play.

Method 3

I could not find evidence of using this method in the Core. It looks like a hack, to be honest. Here's the method:

$itemQty =  $order->getItemsCollection()->count();
$shipment = Mage::getModel('sales/service_order', $order)->prepareShipment($itemQty);
$shipment = new Mage_Sales_Model_Order_Shipment_Api();
$shipmentId = $shipment->create($orderId);

Step 1 is exactly the same as Method 2 above. No difference. However, you get back a $shipment object, which is replaced by a direct insantiation of Mage_Sales_Model_Order_Shipment_Api. This is non-standard. The best-practice way of getting a shipment Api object would be to call Mage::getModel('sales/order_shipment_api').

Next, it uses that overwritten, new Shipment API object to create a shipment from an $orderId variable that hasn't been defined in your code. Again, this seems like a workaround.

Looking at Mage_Sales_Model_Order_Shipment_Api::create(), it seems like a one-stop-shop for generating a shipment as the most basic details needed to create the shipment is only an order increment_id.

This is a hack that shouldn't be used by any module or extension. This API is meant to be consumed by features exposed via XML RPC / SOAP API requests and is intentionally basic to eliminate multiple step API requests.

Eventually Method 3 gets to the nitty-gritty, though, and via a call to Mage_Sales_Model_Order, it calls prepareShipment, which is a higher-order abstraction for the familiar Method 2 above:

public function prepareShipment($qtys = array())
{
    $shipment = Mage::getModel('sales/service_order', $this)->prepareShipment($qtys);
    return $shipment;
}

Key differentiator here - if you need a shipment, don't mind hacks, and only have an increment_id - use this method. Also useful information if you prefer to handle this via the SOAP API.

I hope that helps.

The code under Mage_Catalog_Block_Product_Abstract has a very useful comment.

/**
 * Retrieve url for add product to cart
 * Will return product view page URL if product has required options
 *
 * @param Mage_Catalog_Model_Product $product
 * @param array $additional
 * @return string
 */
public function getAddToCartUrl($product, $additional = array())
{
    if ($product->getTypeInstance(true)->hasRequiredOptions($product)) {
        if (!isset($additional['_escape'])) {
            $additional['_escape'] = true;
        }
        if (!isset($additional['_query'])) {
            $additional['_query'] = array();
        }
        $additional['_query']['options'] = 'cart';

        return $this->getProductUrl($product, $additional);
    }
    return $this->helper('checkout/cart')->getAddUrl($product, $additional);
}

The difference is that the Mage_Catalog_Block_Product_Abstract::getAddToCartUrl will set the url as the product view page if the product has required options, otherwise it will just return Mage_Checkout_Helper_Cart::getAddUrl.

The getAddToCartUrl can be used when you are not on the product view page, say for the wishlist page. So that you do not get an error when the user tries to add a product to the cart that has required options.