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Currently I enroll in Second Course in Abstract Algebra. I don't think I perform well (Two Mid-Terms show that I am in the 50% percentile range which will probably lead me to a B/B+). So I am wondering is it a good idea to switch the grade option from Letter grade to Pass/No Pass? Will it hurt my academic credibility when I apply to grad school after graduation?

As a freshman, I didn't realize that there is a gap between First Course in Abstract Algebra and Second Course in Abstract Algebra(Galois and Module Theory) when I registered the course. Is it possible for me to take some more advanced Algebra Courses in the future (For example taking the graduate level Course-Group Ring Fields when I am a Junior/Senior) to offset the negative effect of P/NP of Second Course in Abstract Algebra?

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Since you're in your first year, it won't make a huge difference either way. I'd be tempted to stick with the B, since readers of your transcript may well interpret a P as concealing a much worse grade, but as long as you succeed in more advanced courses I wouldn't worry about it.

Kevin Carlson
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