If your directory contains any links about gambling, p0rn, or other niches that are not allowed in adsense then it is a violation and you will get banned. I know a guy who got banned doing this.
i suggest getting an adsense account under a business name and ip address etc so if you get banned just sign up again with different stuff
newbie191 made a good point here. If those section exists in your page. I believe there should be no ad blocks on those specific pages. So far I didn't see any thing illegal on your site. So I guess you are good to go. Just a note, You might want to improve the design of your site.
I have never used adsense on any of my directories including even article directories but yes you are allowed to do so. But take care of reviewing links or articles as those are user submitted contents and might harm your adsense profile instead.