The sending state tells you whether the message was only prepared, accepted by the sending server, still waiting or rejected. An email prepared in the extension stays prepared until HawkOpen has stronger evidence, because preparing a message does not prove it was sent.
Replies are detected on the Pro and Business plans by checking the connected mailbox. On those plans you can also set alerts, for example when there is no reply after a number of hours. The free plan has one fixed rule: an alert when there is no reply within 24 hours.
Browser notifications from the extension and the dashboard come for replies, bounces, unsubscribes and fired alerts; a single open or click does not send one. Opens by Apple Mail, Gmail’s proxy or a scanner are listed with their category and never fire an alert.