Is it illegal for a PE teacher to take basketball lessons in his spare time through a contract?

It's not illegal. According to relevant information, the Ministry of Education prohibits teachers from paying tuition outside during winter and summer vacations or holidays, which refers to subjects such as senior high school entrance examination or college entrance examination, such as physical chemistry outside Chinese. Basketball is not one of them. Basketball is just a way of exercising or hobbies. Therefore, it is not illegal for some PE teachers to teach basketball outside, as long as it does not affect the normal teaching work.