Get notified by email when Fatal error occurs on wordpress site?

I think you are misusing shutdown hook. WP attaches it to use with register_shutdown_function() and it’s meant to process end of script execution, not log/process errors.

If you want to handle errors in a custom way you are better off using generic PHP set_error_handler() which is meant for that.

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)