Would my note or comment need to be an entirely separate article, or could I submit a scholarly writing from a class as my contribution to the Law Review?
Short answer: entirely separate article.
Long answer: Unfortunately, law review members are not able to submit a paper as their article that was written in conjunction with a class. However, I think this is a good thing. Writing an article about a topic that you are passionate about is a completely different experience than writing a paper for a class. If you were still wanting to take a scholarly writing class, you can still take it for another SW credit, or you cannot take it for SW and just take it normally, writing only a 10 page paper or taking an exam (that's what I did when I took a scholarly writing class because it sounded interesting).