You have to be a writer on a professional level to write something for About.com. And from what I've seen so far, they don't link out from their pages at all.
Yes I am pretty sure once you become an author with them you are not allowed to link out unless the site is one the allow out linking to. All of the links are no follow either way also from what I have seen.
If you have the expertise to become a writer for about.com, then you are certainly wasting your time getting links from them. You should be disseminating content like crazy for all sorts of news and educational outlets to get high quality backlinks.
You can also ask the person who writes for the category to include a link to your site. But you need to have something really worth linking to. They are compensated by Ad Revenues and outgoing links to 3rd party sites don't make them money.
Many links are follow links. Each about.com 'expert' has a little latitude with linking policy. Getting links is not easy but is also not impossible. I've even found forums on about.com that allow follow links for first time posters!
Yes I am pretty sure once you become an author with them you are not allowed to link out unless the site is one the allow out linking to. All of the links are no follow either way also from what I have seen.