We present non-volatile memory (NVM) devices based on valley-spin hall effect (VSHE) in monolayer WSe2 and discuss how we utilize their unique properties for logic-memory integration in two applications: (i) compact and low power crossbar arrays capable of performing matrix-vector multiplications for binary neural networks (computing integrated within a memory macro) and (ii) energy-efficient non-volatile flip-flops (NVM integrated in logic) for energy autonomous systems. We discuss the appealing attributes of the VSHE-devices enabled by coupling WSe2 with perpendicular magnetic anisotropy (PMA) magnets and show their utility in mitigating the design conflicts of memory devices. We show how the true and complementary bit-storage along with the integrated back gate of VSHE-devices enable the design of compact and low power compute-enabled NVM arrays for binary neural networks. Further, we utilize the VSHE-devices to design non-volatile flip-flops, which feature low power data backup (by virtue of VSHE-based write) and robust restore operation (due to differential data storage in a single VSHE-device).