Is the director of the Planning and Finance Department of the Health Bureau high in rank? What does the Planning and Finance Division of the Health Bureau do?

This depends on the level of the health bureau. If it is a health bureau of a municipality directly under the Central Government, its planning and finance department is at the division level. In prefecture-level cities, it is generally at the deputy division level. In county-level cities, it is at the division level.

Their functions were copied from the Internet:

The organizational functions of the Planning and Finance Department of the Health Bureau

Formulate the city's health development plan, guide regional health planning work, and coordinate Plan and coordinate the allocation of health resources in the city; study and propose the price construction of health services in the city; be responsible for the city's health statistics, infrastructure, and medical equipment management; be responsible for the finance, accounting, fixed assets supervision, management and auditing of directly affiliated units.

There will be certain differences among regions and units.