Are banks and schools institutions? Do I have to go back to my hukou to work in these institutions? What exactly does "three supports and one support" mean?

Banks are not, nor are some private schools. Going back to your registered place to work is an ancient calendar, unless you are entrusted.

The "three supports and one support" program for college graduates was jointly initiated by the Central Organization Department, the Ministry of Personnel and the Ministry of Education. Since 2006, it has been implemented for five consecutive years, and the country will recruit 20,000 college graduates every year, mainly engaged in teaching, supporting agriculture, supporting medicine and helping the poor in rural areas (referred to as "three supports and one support"). The service period of "three supports and one support" college graduates is 2 years. During the service period, the living allowance, transportation allowance, personal accident insurance and hospitalization medical insurance expenses required shall be paid by the special funds arranged by the autonomous region.

The specific work is: supporting agriculture, teaching and supporting doctors, sponsored by the state, all over the country. According to the situation reported by various places, you can apply for the exam, which is generally available on the provincial postgraduate information network. After serving for two years, if you want to take the postgraduate entrance examination for civil servants, you can get extra points. The civil service exam is 4 points, which is a considerable score. In principle, it is assigned to the village after being admitted to the three supports and one support, but generally they stay in the town government to work, and their work is relatively easy. At present, the competition of "three supports and one support" is fierce, and it takes some efforts to apply for the exam, because this is the only curve and the best way to be a civil servant, and the relationship is very intense. Generally, if your home is there, you should apply for three supports and one support, so as to be competitive.