Change the HTML of the comment form that is generating somewhere from the core WordPress

You can write your own custom HTML structure for comment listing. Inside your comments.php file, there will be a call to wp_list_comments() function. Find it, and pass your own function as its callback:

wp_list_comments( array( 'callback' => 'my_function' ) );

Now, create a callback function and start implementing your own HTML structure. This function accepts 3 arguments. Here is a basic example:

my_function( $comment, $args, $depth ){
    $GLOBALS['comment'] = $comment;
    // You have access to comment's ID and other
    // comment query methods here, such as comment_ID();
}