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We report a comprehensive study of single crystalline free-standing PbZr_0.2Ti_0.8O₃ (PZT) and PZT/(La,Sr)MnO₃ (LSMO) membranes on different base-layers, including Au, LSMO/SrTiO₃ (STO), and 2D semiconductor MoS₂. We deposit 10 to 50 nm epitaxial PZT thin films on Sr₃Al₂O₆ (SAO) or LSMO/SAO buffered STO substrates using off-axis RF magnetron sputtering. After water etching of the SAO buffer layer, we transfer the suspended oxide membranes on designated base layers. We create stripe and dot shaped domains in the PZT and PZT/LSMO membranes and analyze the domain wall roughness and creep behaviors via piezo-response force microscopy, which reveals long range random bond disorder dominated behavior and substrate-dependent dimensionality. We then fabricate 2D MoS₂ transistors sandwiched between 50 nm PZT membrane top-gates and SiO₂ back-gates. Switching the polarization induces nonvolatile current switching in the MoS₂ channel, with a current on/off ratio of ~2.04×10⁵ achieved at room temperature. The PZT membrane top-gated MoS₂ transistors exhibit long retention for over 3 days in both on and off states and robust cycling behavior, making them promising for developing flexible nonvolatile memory applications.