What categories are indexed by search crawlers?

When I change my Settings to edit robots.txt to allow indexing by search engines, which Categories are indexed?

Can I create a private category either only for me or only for Admins which is not indexed for search engines and also is not indexed on the Discourse internal search engine?

Any category that’s viewable without logging in can be indexed (it’s up to the search engine whether or not they do index it).

Yes, search engines can’t see content that requires a log-in… so private categories are not indexed. Only users with permission will see search results for that category within Discourse.