What you are seeing are not errors or warnings, they are notices…
Notice: Undefined index: _R in /www/bionomic/www/htdocs/wp-content/themes/parallelus-razor/framework/utilities/email-functions.php on line 108
Notice: Undefined index: _S in /www/bionomic/www/htdocs/wp-content/themes/parallelus-razor/framework/utilities/email-functions.php on line 114
Notices do not affect the execution of PHP in any way, they are just notices. Very often PHP notices mean nothing, i.e. they report issues that are not actually issues. If you don’t want to see these notices then you will need to set WP_DEBUG to false in your ‘wp-config.php’ file. Once you have done that the contact form should work properly. (It is the notices being returned after the form is submitted that is preventing the AJAX script from seeing the “success” string and then displaying the “thank you” message.)