What is the alternative to drupal_realpath()?
To get the HTTP path of a file, you need to use file_create_url($uri).

file_create_url('public://php_includes/functions.php');


This will output http://mysite.com/sites/files/php_includes/functions.php.

Regarding the fact that drupal_realpath() is deprecated, I think it's to warn developers to avoid relying on file system path and instead use wrappers.