In an effort to automate a website, I’d like to add location and a custom field (e.g. country flag) to the groups. I could then fetch the groups via the JSON representation (https://forum.fairphone.com/g.json) and directly generate the map and the website.
Please give groups some love. 
Yeah I’ve been thinking about this a lot lately. Group UI/UX definitely feels like an outlier to much of the app. Something like custom user fields but for groups could be really useful.
The fact that the main group listing scrubs HTML in the description makes it hard to add additional items to use for CSS styles, too.
In the main groups listing I needed to show some “tags” for the various groups so I resorted to renaming them to sort the “groups of groups” how I wanted, and using some CSS hacks on the ‘href’ selector to add some content with a little color label so people can easily tell the types of groups apart.
Groups, like topics and posts, have support for custom fields, and it can be exposed by custom plugins.
Is it possible for Admins to simply add a custom field, like they can for users (e.g. Admins added a field for the phone model her at the Fairphone Forum)?
There is no UI for that at the moment. You need a custom plugin to use those.
Is there such a “custom plugin”? Or does “custom” mean that one has to do this on one’s own?
It means you need to write one yourself or commission one in the marketplace.