Which template used for adding nodes I want to add some custom checks to all of my Drupal pages (except the administration pages).

I am using Bartik theme that comes with Drupal 7.26

I added the custom check in node.tpl.php and the check worked for all urls of type /node/%

However, I also want to add this check for node add, edit and delete pages.
I cannot do this.

What I have already tried:
-> Creating a node--add.tpl.php in bartik folder and adding check there.
-> Creating a custom module, and using hook_menu to route /node/%/id to a custom page.
-> Adding this function

function bartik_preprocess_page(&amp;$vars, $hook) {
  if ((arg(0) == 'node') &amp;&amp; (arg(1) == 'add' &amp;&amp; arg(2) == 'product')) {
    $vars['template_files'][] =  'node-add-product';
  }
}


in my bartik template.php file. After adding this function I created node-add-product.tpl.php file and added check there.

For all the methods I have tried, the node creation page does not change at all.

I also tried creating page--node--add.tpl.php. Then the custom check works. But the header, footer, and sidebars disappears. (Only node creation template is rendered)
I think you are using the wrong tpl file to edit the node/add/[content-type] form.

You need to create (if I remember correctly) a [content-type]-node-form.tpl.php and add the required elements you wish from there. See here for more details: 

https://drupal.org/node/1092122