With the emergence of cutting-edge hardware systems such as cloud computing, edge computing, and on-chip neural network accelerators, how to design advanced memory strategies to substitute the traditional ones for maximizing the potential performance of non-volatile memory (NVM) under the existing hardware conditions, has become an urgent research issue for both academia and industrial communities. It is promising and innovative to improve computer systems in the layer of data exchanging with the emerging advanced semiconductor devices. In the paper, to address the inefficiencies of write-intensive, high power consumption, low hit rate and so on, which exist in hybrid Magnetic Random Access Memory (MRAM) cache systems, three novel cache replacement strategies and two cache prefetching strategies are put forward. The proposed triple novel replacement strategies, including historical frequency and time judgments, duplicate data-aware deletion, and dynamic relevance factors computing, can be utilized to compensate for the shortcomings of the traditional Least Recently Used (LRU) replacement strategy, respectively. In the two novel prefetching strategies, region distribution parameters and Listnet ranking network are imported into the caching process, respectively, to achieve optimized hitting performance. The simulation results demonstrate that the proposed replacement strategies can achieve up to 61.76%, 84.91%, 56.49%, and 53.21% optimization of write count, hit rate, dynamic power, and IPC compared to the conventional one. The proposed prefetching strategy can achieve up to 91.27%, 49.25% hit rate and IPC optimization. Meanwhile, the synthetic evaluation of the replacement and prefetching strategies are elaborated in the paper, including multi-core characteristics, information entropy, interplays and the performance constraints between replacement and prefetching mechanism, which would facilitate more credible ideas for future memory inefficiencies management and strategy design.