The answer is rather the same as [this earlier inquiry](https://meta.stackexchange.com/questions/56075/how-to-get-question-badges-in-cw-mode), but the system did change, and with it how Community Wiki affects badges. Not the ones you asked about, though.

**Badges like Nice/Good/Great Question/Answer can be awarded to Community Wiki posts**. This is because Community Wiki only stops reputation, not post score, and those badges only care about post score. The new system has not affected this.

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Technically, badges still don't care about Community Wiki *directly*. The only badges that are affected by Community Wiki are the ones like Epic (dependent on reputation caps that you can't hit on wiki posts), as well as the Generalist and tag specialist badges (dependent on tag score, which [disregards all votes on community wiki posts](https://meta.stackexchange.com/questions/52754/how-is-the-score-on-the-top-users-page-calculated/52792#52792)). Well, actually, Generalist and the tag specialist badges do specifically mention the "non-wiki" clause, but that strikes more of a formality than as if it were an extra special requirement. The criteria just to award them already implicitly requires posts to be non-wiki.

Recent in this is that specialist badges awarded for performance in tags *are now revoked if you drop below it*. This means that if you were to get those badges, but then some of your posts were turned CW to the point that you no longer qualified, you would lose those badges.