node_view does not show the comments box I am using node_view(node_load($nid), "full") and I print(render()) the result in a template. But the content of the node is appearing but not the comments nor the comments form. How can I display them ?
You probably need to use the node_show() function instead; it outputs the node as well as its accompany comment thread and comment form. node_show() relies on node_view() to print the node itself, but also calls comment module's code to build the rest.

One good rule of thumb for tracking down these scenarios is to visit the api.drupal.org site, look up the function that you're using to output a portion of the information you need, and look at the functions that also call it in Drupal core.