Please follow the instructions below:
1) Please check the plugin settings '/wp-admin/admin.php?page=contact_form.php' => 'What to use?' => change the lines from wp-mail to mail and vice versa.
2) email messages can be marked as spam on the server. Please choose another email instead of the admin's one ('Use this email:' block) - for example, gmail or similar. If the message is sent, it means that email filtering is set on your server.
3) you should install an extra plugin called WP-mail-SMTP and configure it. Afterwards you should send a test email from this plugin and you will see if the plugin logs have errors. Please view the logs after sending a test letter WP-mail-SMTP and fix the occurring errors. Please pay attention, that it is necessary to set WP-mail-SMTP the same way your contact form is set before sending a message.
BestWebSoft Support Team