To your second question, depends on what bracket of schools your applying to honestly. For top 10 schools this won't be significant in and of itself. Many students who apply to top 10 schools have taken graduate courses as an undergrad and have done well in them. You might be better off doing research and getting results that are publishable or can be presented at a conference. This would look better than an extra course to be honest. There is an undergraduate conference at Ohio state(Young Mathematicians Conference...) I believe. This is something you can look into. I would frankly start doing research this semester if its at all possible to get a head start.
Also doing research with a professor if all goes well could lead to a strong letter depending on your performance. Strong letters of recommendation speaking highly of your research potential are more important than anything else. If your letters are generic and only speak about your ability to do coursework they won't distinguish you from any other applicant. Now if you have A+ grades in a significant number of your math courses then this is less of an issue because it would indicate your the top math student in your cohort at your school. As long as the rigor of the coursework is up to part with tier 1 institution you have a good shot at any school to be honest. But again very speculative since I don't know much about you or your background. Just some general information.