Can I make a notification on the web if buzzer active?
You can make the Arduino, with ethernet shield, act as a server, and serve up a page that contains static content that tells whether, or not, the buzzer is squawking its fool head off.
You can make the server respond to GET requests. A GET request could cause the buzzer to be shut off.
But, the status of the buzzer can NOT be pushed to client(s). The client(s) MUST ask. You can include meta tags that define how often the client(s) re-request the status of the buzzer.