Reworking a Homework Project to Publish as Research During the final year of my Undergraduate degree, I did a literature review as part of a technical writing class to answer a relevant question in Mathematics Education.

I would like to rework the paper (to make it more geared toward the research community) and submit it for publication in a Math Education journal that accepts literature reviews. I would like to do this because 


I believe it would contribute to the field--the question is important, and there aren't any current, comprehensive literature reviews about it (that I know of, and I have spent many hours searching)
I am applying to graduate school soon and I would like to do education research during graduate school 


I have two questions:


Are there any problems with my plan--legally, culturally, or otherwise? I have already spent a long time looking through my former Universities' policies, and I can't find any policies disallowing it. 
If I submit the paper, do I list the University I was at when I did the work as my affiliation?
Chances are your plan is fine. You created the piece of work, and you weren't funded, so there's nobody else that can claim that as his or her intellectual property. Still, I would suggest working with an academic over this - probably the person who set the homework problem. If there's a potential issue with your plan, he is likely to know; further, he can offer you critical comments to get your work up to scratch (writing a literature review is quite different from a homework assignment), and if he's willing to add his name to the paper that adds a lot of credibility to it. He might even be able to suggest a journal for you.

As for affiliation, yes, you list the university you were at since that's where you did most of the work.