Second, you should not only find ways to communicate with the teacher, but also read his papers and have your own opinions if you plan to get in touch with the teacher very early, and then pick some questions. Then you can send an email to the teacher and ask him questions. Of course, you should make sure that your questions are worth answering. Don't ask questions that can be clarified by looking up any information casually, and don't ask questions that distort the original intention excessively.
Third, if the teacher replies to the email, after several emails, you should judge what the teacher thinks of you. If it is good, you can mention your love for this major in this school at an appropriate time to show your determination. It's best to talk about your future research direction. Teachers depend on this.
Fourth, if the teacher doesn't reply to the email, you can send more letters to show your sincerity.
If you can't find the e-mail, you can ask the graduate students or undergraduates of that school to know more about the situation, and maybe you can know more information.
6. Finding a tutor is not a necessary condition. High test scores and excellent professional quality are the king. Without this, it's no use looking for a tutor. If you want to cross the exam, you should spend more time on professional courses!
Work hard!