Tips for learning the language and college/general tips

For context, I'm from the United States.

I'm currently in high school, going into my last year, and since about my first year I've been wanting to move to Japan. I've been taking Japanese for three years, and I'll be taking it for my final year, so I already have support from that, but I feel like I'm not learning quick/well enough, so I'd like to know any books, study guides, or anything of the like I can use. I'd also like to know any colleges or universities that are good for degrees in applied mathematics. Speaking of college, I have long hair and earrings(I'm a guy) would it be a good idea to cut my hair short and not wear my earrings at college/work? I'm open to any other general tips or information for moving to Japan.