Automatically wrap post image in div

It’s the image_send_to_editor filter:

if(is_admin()){

  add_filter('image_send_to_editor', 'wrap_my_div', 10, 8);

  function wrap_my_div($html, $id, $caption, $title, $align, $url, $size, $alt){
    return '<div class="mydiv" id="mydiv-'.$id.'">'.$html.'</div>';
  }
}

For existing images/posts you can try the regex in the function below