It is not illegal for an individual to open a calligraphy class at home, have a business license and register with the Industrial and Commercial Bureau. 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.
It is illegal to start a remedial class without a license, and you will be fined and disqualified. In violation of laws, regulations and relevant provisions of the state, the education administrative department shall revoke it. If there are illegal gains, the illegal gains shall be confiscated.