I'm not sure there would be much benefit in the last point over the current behavior, which is a noindex flag on empty content. In all honesty, if you have an existing category with no content and no listings, then why does the category even exist? These categories should be deleted or be given content. What's the point of creating them just to save them for later? How are the categories being visited/crawled if they have no members? Perhaps these links should be updated.
This situation could apply to any kind of content, and Google would equally take offense at those pages (e.g. a regular wiki page with no content). But again, such pages are already flagged as "noindex."
As for categories with 1 or 2 or 3 entries, I'm not really sure what's so wrong about that, if it makes sense in the context or state of your wiki. If Google complains there's not enough content, why not just add some content explaining the category? It would be better all around. If the category has utility, then e.g. doing a blanket hide of all categories with fewer than 4 entries would actually be a detriment to users. Sometimes it may be a regular page that was mistakenly treated-as a category, when it has regular content; hiding such a page automatically might not be desired.
Another thought is that many of Google's tools are a service intended to help the webmaster identify potential issues and correct them. If you start hiding swaths of content from those tools, you are even less likely to address them.
If you want to emulate this behavior, consider moving "bad" categories to a special area where guests don't have permission to view contents. When the category gets enough listings, move it back to a public location. In this way, you can review the categories and see if there's a better solution than just hiding them.
In summary, thinking about it only in terms of categories and number of listings is considering the problem too narrowly. What about books, or areas, or feeds, soon disambiguations, etc? They all treat listed pages slightly differently; hiding may or may not be appropriate for each, nor for future containers. Number of listings alone may be a factor, but how would it be weighed against other factors (e.g. having fully-developed text content), if at all, when hiding them?
Another thing I worry about is the area listings for areas that I assume are inundated with "empty categories", or you would not be requesting this. Calculating the number of category-listings accurately would not be possible when performing the query there, but would be done in a later step once the category-data has been loaded (and even that is an estimated value). It is likely that many, and sometimes all, the listings in the area would be hidden on a given navigation-page, while the navigation-page itself is not hidden. So even though Google has permission to view the area list, you would then have Google complaining that area-list page 5 has no content. This is another reason why moving the categories you want to hide to an area that actually is hidden may be the better solution.