What is higher a blue belt or a purple belt?

The purple belt is higher in rank than the blue belt, but of course some schools don't have a purple belt, so there you advance straight from blue to red. Just as a key of advice for differing between belt ranks the darker the belt most likely the higher the rank.

That depends on the school and style in question. My style does not have purple or blue belts. In some schools, blue is the highest rank (instead of black).