Hello,

normally you have to monitor your preferred domain in Google Webmasters tools.
For example if you have the site working with both version www. and non www you have to put both in webmasters tools to validate the property of both sites, then choose the preferred domain in webmasters tools settings.

About http/https you should choose and monitor only one based on your preferred site version. If you want that the site will be used/indexed using http or https.

Probably better informations can be found on the Google support docs: https://support.google.com/webmasters/answer/44231?hl=en

John