Is Haikou Xinhai School directly under the municipal government?

Not a municipality directly under the central government. Official website of Haikou Xinhai School shows that Haikou Xinhai School is a school directly under Hainan Province, not a school directly under Haikou City. Xinhai School is one of the key middle schools in Hainan Province, which is directly managed by the Education Department of Hainan Province. The competent unit of the school is the Education Department of Hainan Province, which does not belong to the schools directly under Haikou City.