If you are looking for a readymade solution, I believe you can only enable notification for the admin for new questions. However, users who have already asked a question and the user who has already answered should get an email notification automatically as it is a built-in functionality out of the box. You should check the admin settings.
If that is not the case and you are looking for a custom solution, you might need to create a plugin that triggers events on respective user interactions.
Have a look at the following links. You may have to use the Event module and qa_send_notification($userid, $email, $handle, $subject, $body, $subs) to send notifications to the respective users.
If you are looking for an email subscription feature, you can follow the above method to send email notifications to users who subscribe for new questions.