Is it appropriate for the teacher to visit 500 yuan at home?
Not appropriate. According to the government portal of the Ministry of Education in People's Republic of China (PRC) (China), school teachers are not allowed to accept red envelopes and gifts from their parents. Parents who want to be close to the teacher can give the teacher some small gifts, such as local products, flowers, etc., and they can also express their wishes to the teacher if they are not expensive.