Problem to show custom post type in archive page category wise

You need to check the information that their is in action variable.

$action =   (isset($_REQUEST['ac'])) ? $_REQUEST['ac'] : 'none';
var_dump("action: "+$action);

With this line, you will be able to review it’s content and you will see that you don’t get the correct information.
I guess that your dev database is out off synch with your local one.

So, you need to create post/page/categories to review your code.
Otherwise, I’m using a really nice plug-in to migrate your local to dev DB.

Note: don’t forget to push your uploads too =)