Is it bad, in terms of SEO, to submit the same site twice in the same directory? Like I submit the site under Nutrition and then under Business.
I don't think so, its not bad at all. In fact it will help more to submit your site in most relevant category. If your got site which can fit into more than 1 category, then you can submit in different categories. But only Paid Directories would allow you with such submissions. It would be much better if you add inside pages (sub-folders or sub-domains) of your site in the entire directory's multiple categories.
i personally don't allow any subpages on my directory most directory owner does not, and they don't like your website in more than one category as well.
In most of Paid Directories, you will see, they allow inside pages or at least sub-domains of a site.
Also, do search engines prefer a site with more pages over a site less pages (assuming everything is the same: keyword density, # of links, meta tags, etc)?
No difference, Best miler. Search engine prefers if there are more inbound links into your site, rather than outbound links. (however, on second thought, I do agree search engine may be susceptible to sites with multiple pages, but some sites have proven that wrong).
sometimes editors dont allow multiple entires for same site . most of the free directory owners dont allow deep linking .