The Board shall serve without compensation and shall (1) hear appeals from any nonexempt employee who has been suspended longer than five days, dismissed from the municipal service, or demoted to a lower grade and salary; (2) hear appeals concerning rejection of applications for employment and the conduct of examinations; (3) establish its own rules and procedures governing the conduct of the Board's business; and (4) make such investigations of municipal personnel practices as it deems necessary to carry out its responsibilities.