Currently in the Comments section, if you (the admin) wants to reply to a pending comment, perhaps to warn them or whatever, the only way to send the reply is by clicking ‘Approve and Reply’.
Is there a way to send a private message to the submitted email address (besides manually writing an email) before approving the comment?
No, there is no way in the WordPress Core to send private messages. That’s what the email address is for. But why would you want an extra contact form for that?