The computer running Monocle Gateway does not need a public IP address on the Internet. It can certainly be a private IP address inside your network behind your router/NET. It does however require outbound Internet access to communicate with the monocle services. This computer also need to be accessible on your network from the Alexa devices. The Alexa devices will talk to the Monocle Gateway when requesting camera stream rather than talking to your IP cameras directly.
Another question, if I change the Monocle settings on the official website, do I need to generate a new token?
No, settings are communicated for each camera stream every time the camera stream is requested/triggered from Alexa. We do suggest generating a new token if your IP address changes on the computer running Monocle Gateway. It’s not required but it can take up to 24 hours for the new IP address to get propagated in the DNS record. Thus a new token speeds this process up by issuing a new DNS record fore your Monocle Gateway instance.
Thanks, Robert