Here's what you should be seeing:
OR, if you have "Interest sync" enabled:
Words (Note that Mailchimp does not make this terribly easy to refer to as they have changed the words they use, and also because they use "group" and "grouping" interchangeably)
Mailchimp list - these are now called Audiences at Mailchimp. Nb. Mailchimp is heavily pushing people towards only having one "Audience" (List) and using the following to segment within that list.
Mailchimp [interest] grouping which is a set of...
Mailchimp groups - a list member at mailchimp can be in one or more groups within each grouping. Mailchimp's own forms can be configured to allow members to edit these themselves.
CiviCRM group - self explanatory, but just including to show the distinction between Mailchimp group and CiviCRM group!
The extension requires that you have a "membership group" in CiviCRM which will determine whether someone is subscribed/unsubscribed in the selected Mailchimp audience/list. Optionally, after this, you can sync other CiviCRM groups with mailchimp interest groups within that audience. Adding somone in CiviCRM to a group that is mapped to an interest group does not in itself add them to the list; you need to add people to the group used for membership, too.
It's not clear from your question exactly what you're trying to achieve. If you're trying to sync up an audience called Green Gazette with a CiviCRM group so that adding someone in Civi will add them in Mailchimp (and vice versa), then you should select the "Membership Sync" option, then select your list.
CiviCRM remembers which Mailchimp list/audiences and Mailchimp groups are configured by storing a unique ID from Mailchimp. If you delete that audience/group at Mailchimp that link will be broken.
If you get that error message after doing this, but you've been playing around a bit, I would advise just trying edit and saving the CiviCRM group settings again to see if it's repeatable - I know that some of those messages get added to the session at awkward times so can occasionally display at the wrong time. If you've selected a list but when you press save you always get that error, that sounds like a new bug.
Personal note: the current mailchimp integration (link) has some limitations that I have discussed in my proposed new mailchimp sync extension. Everyone should feel free to comment (issue queue/PR) and input on my plans there.
EDIT (following your edit with screenshot)
It looks like you're seeing the CiviCRM custom field group fields in the normal CiviCRM way. This means that the .extra.tpl file is not firing; it's not loading in the mailchimp settings template file
.extra.tpl files are deprecated these days; the extension needs updating to use the Regions API. I'm not sure which version of CiviCRM you're using; it's entirely possible that they removed
.extra.tpl files or somehow otherwise changed something that means the required template addition is not sourced. I'd start looking there (and also check for JS errors). Interesting that it works for new groups, though.