Hair in Japanese schools?

so i'm thinking about becoming an exchange student in japan next year and i heard that there's rules regarding hair and the length. my hair's pretty long, it comes to my belly button. haha. anyway, is it true that they make you cut it if it's too long? or do they not enforce that kind of thing anymore? oh and another thing, i heard hair dying isn't allowed. i don't dye my hair, but the sun has bleached my hair a bit, soo my natural hair color is a dark shade of brown with like auburn, but cause of the sun, my hair's like light brown and different shades of brown and people usually asume that i dyed my hair. is this a problem? i'm korean btw, but i'm also part russian not that anyone can tell. haha.