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.

OK, your request is not difficult to implement, see my solution. It works only when you create shipment using Magento admin panel. I supposed that shipments are created manually.

1. Create local module (ex. ShipmentSplit) and rewrite Shipment controller, config.xml:

<?xml version="1.0"?>
<config>
    <modules>
        <Some_ShipmentSplit>
            <version>0.1.0</version>
        </Some_ShipmentSplit>
    </modules>
    <admin>
        <routers>
            <adminhtml>
                <args>
                    <modules>
                        <Some_ShipmentSplit before="Mage_Adminhtml">Some_ShipmentSplit_Adminhtml</Some_ShipmentSplit>
                    </modules>
                </args>
            </adminhtml>
        </routers>
    </admin>
    <global>
        <helpers>
            <some_shipmentsplit>
                <class>Some_ShipmentSplit_Helper</class>
            </some_shipmentsplit>
        </helpers>
    </global>
</config>

2. Create Configuration settings to enable/disable splitting functionality and store weight threshold parametr, system.xml.

<?xml version="1.0"?>
<config>
    <sections>
        <shipping>
            <groups>
                <splitting translate="label">
                    <label>Shipment Splitting</label>
                    <frontend_type>text</frontend_type>
                    <sort_order>10</sort_order>
                    <show_in_default>1</show_in_default>
                    <show_in_website>0</show_in_website>
                    <show_in_store>0</show_in_store>
                    <fields>
                        <enable translate="label">
                            <label>Allow Shipping to Split</label>
                            <frontend_type>select</frontend_type>
                            <source_model>adminhtml/system_config_source_yesno</source_model>
                            <sort_order>1</sort_order>
                            <show_in_default>1</show_in_default>
                        </enable>
                        <weight translate="label">
                            <label>Maximum Weight</label>
                            <frontend_type>text</frontend_type>
                            <validate>validate-number</validate>
                            <sort_order>2</sort_order>
                            <show_in_default>1</show_in_default>
                            <depends>
                                <enable>1</enable>
                            </depends>
                        </weight>
                    </fields>
                </splitting>
            </groups>
        </shipping>
    </sections>
</config>

3. Rewrite Shipment controller:

<?php
require_once 'Mage/Adminhtml/controllers/Sales/Order/ShipmentController.php';
class Some_ShipmentSplit_Adminhtml_Sales_Order_ShipmentController extends Mage_Adminhtml_Sales_Order_ShipmentController
{

    public function saveAction()
    {
        $enableSplitting = Mage::getStoreConfig('shipping/splitting/enable');
        $isNeedCreateLabel = isset($data['create_shipping_label']) && $data['create_shipping_label'];

        //if splitting not enabled use standard magento logic
        if (!$enableSplitting || $isNeedCreateLabel) return parent::saveAction();

        $data = $this->getRequest()->getPost('shipment');
        if (!empty($data['comment_text'])) {
            Mage::getSingleton('adminhtml/session')->setCommentText($data['comment_text']);
        }

        try {
            $shipment = $this->_initShipment();
            if (!$shipment) {
                $this->_forward('noRoute');
                return;
            }

            $comment = '';
            if (!empty($data['comment_text'])) {
                $shipment->addComment(
                    $data['comment_text'],
                    isset($data['comment_customer_notify']),
                    isset($data['is_visible_on_front'])
                );
                if (isset($data['comment_customer_notify'])) {
                    $comment = $data['comment_text'];
                }
            }

            $shipmentCreatedMessage = $this->__('The shipment has been created.');
            $labelCreatedMessage = $this->__('The shipping label has been created.');

            //split to groups
            $shipments = $this->_initShipmentGroups($shipment);

            foreach ($shipments as $shipment) {
                $shipment->register();
                if (!empty($data['send_email'])) {
                    $shipment->setEmailSent(true);
                }
                $shipment->getOrder()->setCustomerNoteNotify(!empty($data['send_email']));

                $this->_saveShipment($shipment);
                $shipment->sendEmail(!empty($data['send_email']), $comment);

                $this->_getSession()->addSuccess($isNeedCreateLabel ? $shipmentCreatedMessage . ' ' . $labelCreatedMessage
                    : $shipmentCreatedMessage);
                Mage::getSingleton('adminhtml/session')->getCommentText(true);
            }
        } catch (Mage_Core_Exception $e) {
            $this->_getSession()->addError($e->getMessage());
            $this->_redirect('*/*/new', array('order_id' => $this->getRequest()->getParam('order_id')));
        } catch (Exception $e) {
            Mage::logException($e);
            $this->_getSession()->addError($this->__('Cannot save shipment.'));
            $this->_redirect('*/*/new', array('order_id' => $this->getRequest()->getParam('order_id')));
        }
        $this->_redirect('*/sales_order/view', array('order_id' => $shipment->getOrderId()));
    }

    /**
     * this function splits shipment into groups
     * @param Mage_Sales_Model_Order_Shipment $shipment
     * @return array
     */
    protected function _initShipmentGroups(Mage_Sales_Model_Order_Shipment $shipment)
    {
        /**
         * @var $items Mage_Sales_Model_Resource_Order_Item_Collection
         */
        if ($maxKg = (int)Mage::getStoreConfig('shipping/splitting/weight')) {
            $qtys = $this->_getItemQtys();
            $itemWeights = array();
            $allItems = array();

            $order = $shipment->getOrder();
            $items = $shipment->getOrder()->getItemsCollection();
            /**
             * fetching items weight
             */
            foreach ($qtys as $itemId => $qty) {
                $itemWeights[$itemId] = $items->getItemById($itemId)->getWeight();
                while ($qty--) $allItems[] = $itemId;
            }

            $groups = array();
            $i = 0;
            /**
             * create item groups which every group weight up to $maxKg threshold
             */
            while (count($allItems) > 0) {
                $i++;
                $groups[$i] = array(
                    'items' => array(),
                    'weight' => 0,
                );
                foreach ($allItems as $index => $itemId) {
                    $itemWeight = $itemWeights[$itemId];
                    if ($groups[$i]['weight'] + $itemWeight <= $maxKg) {
                        $groups[$i]['weight'] += $itemWeight;
                        $groups[$i]['items'][] = $itemId;
                        unset($allItems[$index]);
                    }
                }
                /**
                 * check if an item is added to the group,
                 * if not added, it means some product weight is over threshold
                 * you can throw within if or add this product to the group
                 * or you can remove this IF block
                 * if you are sure that all products have appropriate weight
                 */
                if (count($groups[$i]['items']) == 0) {
                    $itemWeight = $itemWeights[$itemId];
                    $groups[$i]['weight'] += $itemWeight;
                    $groups[$i]['items'][] = $itemId;
                    unset($allItems[$index]);
                }
            }

            //print_r($groups);
            $shipments = array();
            if (count($groups) > 1) {
                foreach ($groups as $data) {
                    $groupItems = array();
                    foreach ($data['items'] as $itemId) {
                        if (isset($groupItems[$itemId])) {
                            /**
                             * if same item then only increase quantity
                             */
                            $groupItems[$itemId]++;
                        } else {
                            $groupItems[$itemId] = 1;
                        }
                    }
                    //create shipment for each group
                    $shipments[] = Mage::getModel('sales/service_order', $order)->prepareShipment($groupItems);
                }
            } else {
                $shipments[] = $shipment;
            }
            return $shipments;
        } else {
            Mage::throwException('Shipment package weight not defined');
        }
    }
}

Enter to admin order management page, open order, click [ship] button, click [submit shipment] button (you can except some items giving 0 qty to ship) and our logic automatically create shipments based on weight threshold (minimum one shipment). See my results: