Paging the list of comments, and getting the comment count I am getting all the comments listed in the same page. How can I do the paging concept for comments?
How do I get the comment count?
Paging on comments is provided in Drupal Core without any contribute modules. 

If you go to your content type configuration screen:


D6 Path: admin/content/node-type/[node-type-name]
D7 Path: admin/structure/types/manage/[node-type-name]


You will see there's a Comment field-set/tab(d7) with some options. The option you want to check out is the comments per page setting. Select the number you'll like for when a page should break and save your settings. Once you're comment have pass that threshold you will see a pager for your comments.

Now for the comment counts there a variable available to you in both Drupal 6 and 7 in the node template. The name of that variable is $comment_count.