how to get the count of total comments posted for specific content type including deleted comments too?
You can always dig around the database with a db query with something like:

$content_type = 'mycontenttype';
$query = db_select('comment', 'c');

$query-&gt;join('node', 'n', 'n.nid = c.nid'); //JOIN node with comment
$query-&gt;fields('c', array('cid')); //SELECT the fields from comment
$query-&gt;condition('n.type', $content_type, '=');
$query-&gt;orderBy('c.cid', 'DESC'); //ORDER BY comment id

$num_comments = $query-&gt;countQuery()-&gt;execute()-&gt;fetchField();
$latest_comment_cid = $query-&gt;execute()-&gt;fetchField();


EDIT
In this example I assume you mean unpublished comments and not deleted. See Anil's answer if you want to track count of deleted comments as well.