Due to their unprecedented ability to flexibly manipulate the parameters of light, metasurfaces offer a new approach to integrating multiple functions in a single optical element. In this paper, based on a single-celled metasurface composed of chiral umbrella-shaped metal-insulator-metal (MIM) unit cells, a strategy for simultaneous multiple polarization generation and wavefront shaping is proposed. The unit cells can function as broadband and high-performance polarization-preserving mirrors. In addition, by introducing a chiral-assisted Aharonov-Anandan (AA) geometric phase, the phase profile and phase retardation of two spin-flipped orthogonal circular polarized components can be realized simultaneously and independently with a single-celled metasurface via two irrelevant parameters. Benefiting from this flexible phase manipulation ability, a vectorial hologram generator and metalens array with spatially varying polarizations were demonstrated. This work provides an effective approach to avoid the pixel and efficiency losses caused by the intrinsic symmetry of the PB geometric phase, and it may play an important role in the miniaturization and integration of multipolarization-involved displays, real-time imaging, and spectroscopy systems.