It is same as normal coloured crayfish. Blue colour is caused due to gene mutation. They will eat everything. The male has a red mark on it's claw, but the female doesn't have so.
A blue crayfish is the red crayfishes counterpart. They are small, about 2 inches long and look a lot like little lobsters. You can keep them as pets or you can eat them. If you go to a chinese restaurant you will see them on ice next to the shrimp.
Crayfish is a kind of soft water lobster. It is similar in taste, just a little earthy. You can buy crafish at a fishmonger's, or in the frozen section of a large grocery store. They turn red when cooked.