Is it illegal to run calligraphy classes at home?

Legal analysis: as the case may be. If you have a business license, it is not illegal.

Legal basis: People's Republic of China (PRC) Private Education Promotion Law Article 4 Private schools shall abide by laws and regulations, implement the national education policy, ensure the quality of education, and devote themselves to cultivating all kinds of talents for socialist construction.

Private schools should implement the principle of separating education from religion. No organization or individual may use religion to carry out activities that hinder the national education system.