I'd like to link a YouTube video (from Numberphile) and pose a question about its content. Is it possible to embed the video into the question body?
No, it is not possible to embed the video. You can only link to it.
In principle, the SE platform would allow to embedded videos, but this feature is only enabled on selected sites, not including this one.
If you want to suggest that it is enabled on this site, you could post a feature request.