SEO – Why is Start Page Missing from Sitemap.xml?

you can manually generate sitemap.xml from admin>catalog>Google Sitemap which will resolve missing sitemap.xml issue and also here you find sitemap xml path and

Generally site map is located at yourmagento instance dir

you are getting that url because the homepage is a CMS page.
In your case it has the identifier home.
In order to change that url you need to rewrite the method Mage_Sitemap_Model_Resource_Cms_Page::_prepareObject and make it look like this:

protected function _prepareObject(array $data)
{
    $object = new Varien_Object();
    $object->setId($data[$this->getIdFieldName()]);
    //for home set url to ''
    if ($data['url'] == 'home') {
        $data['url'] = '';
    }
    $object->setUrl($data['url']);

    return $object;
}

of course this won't work if you change the homepage to an other page. But it's a quick way of doing it.
If you want the clean version you have to check what is the hompage for your current store.
For this add a new member and method like this:

protected $_homeId = array();
public function getHomepageId($storeId)
{
    if (!isset($this->_homeId[$storeId]))) {
        $pageId = Mage::getStoreConfig(Mage_Cms_Helper_Page::XML_PATH_HOME_PAGE, $storeId);
        $delimeterPosition = strrpos($pageId, '|');
        if ($delimeterPosition) {
            $pageId = substr($pageId, 0, $delimeterPosition);
        }
        $this->_homeId[$storeId] = $pageId;
    }
    return $this->_homeId[$storeId];
}

In this case, you need to modify the getCollection method in the same class. Before $page = $this->_prepareObject($row); add this:

if ($row[$this->getIdFieldName()] == $this->getHomepageId($store)) {
    $row['url'] = '';
}