The time of each school is different. Most schools start taking exams around the end of August ~ 10 for the first time, and some earlier schools start taking exams around July. The second time is from February to the end of February (there are also a few school exams around March). Make a wish about a month or two before the exam. I suggest that you can contact the professor in advance as long as you don't say that you are not allowed to contact him in advance before making a formal wish. The exam will start from May to July, and volunteers will be given about 1~2 months in advance.