As for the first question: No. The courses you have or plan on taking is at best, a moderate level. It won't really stand out.

As a comparison, I graduated this spring setting the record for the number of graduate courses taken as an undergraduate at my school; this was still not enough for me to crack into the "top 20" schools.
In particular, I covered Dummit and Foote my sophomore year. I went on to cover Hungerford, Issaccs, and a text on universal algebra (personal readings aside). By the way, my main concentration is more topological in nature.

The second question you posed is much more complicated to answer; restricting to algebra is still not enough to say which schools are the "best".

Students, by their nature, will flock to apply to the higher "ranked" schools. These schools have, ofcourse, a very good program. But it may not make sense to go to graduate school at even the very best schools if there is no one studying what you like.

My home institution, the University of Florida for example, is not a very highly ranked school. However, if you want to study finite group theory, there are only a few places in the world that can compete with our faculty members.

To remedy both of the "questions" you have, I would recommend that you study more specialized topics. Try to read research papers, talk to professors, pick up a monograph, do anything you can to find out what it is that you really want to study. This should kill two birds with one stone.

As for myself, I was lucky enough to attend an REU program in geometric group theory. I liked the study, and I applied to the institutions which housed powerful mathematicians in the field. As a reference, I was accepted to UIUC, UC Santa Barbara, Vanderbilt, and a few others. I eventualy chose to go to Vanderbilt; which was the lowest ranking school for which I was accepted. If you look at their faculty, however, you may want to think twice about what rankings really mean.

That said, I know a friend who didn't stand out in school, but entered Berkeley due to his very high GRE score (95, i think).

There are various ways of attacking this procedure, but I hope this helped. Just don't let other people discourage you; mathematics is a beautiful subject, and I have no problem devoting my life to the study. There are many who share the same vision.

Why don't you knock on the door of a couple of algebra professors and ask them what they think? This is probably a good thing to do anyway, since you will need references when you apply to grad school and this is one way to get a professor to get to know you.

Don't be embarrassed - they will probably be glad to hear that someone is interested in their research. If they aren't (and there are some like that) then I would bet they are the kind that don't pay enough attention to their students to tell them apart so it really won't matter anyway.

I really can't believe what that first guy said in his comment. Just because you haven't done much math before doesn't mean you're not good at it. And this whole "you have to be a genius to contribute to math research" idea is complete crap anyway. I think the people who perpetuate this myth are just arrogant guys who think they are geniuses but really aren't.

I would say it in stronger language but I don't know if that's allowed :). Good luck.