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For enhancing transmission performance, privacy level and energy manipulating efficiency of wireless networks, this paper initiates a novel simultaneous wireless information and power transfer (SWIPT) full-duplex (FD) relaying protocol, termed harvest-and-opportunistically-relay (HOR). In the proposed HOR protocol, the relay can work opportunistically in either pure energy harvesting (PEH) or the FD SWIPT mode. Due to the FD characteristics, the dynamic fluctuation of R's residual energy is difficult to quantify and track. To solve this problem, we apply a novel discrete-state Markov Chain (MC) method in which the practical finite-capacity energy storage is considered. Furthermore, to improve the privacy level of the proposed HOR relaying system, covert transmission performance analysis is developed and investigated, where closed-form expressions of optimal detection threshold and minimum detection error probability are derived. Last but not least, with the aid of stationary distribution of the MC, closed-form expression of transmission outage probability is calculated, based on which transmission outage performance is analyzed. Numerical results have validated the correctness of analyses on transmission outage and covert communication. The impacts of key system parameters on the performance of transmission outage and covert communication are given and discussed. Based on mathematical analysis and numerical results, it is fair to say that the proposed HOR model is able to not only reliably enhance the transmission performance via smartly managing residual energy but also efficiently improve the privacy level of the legitimate transmission party via dynamically adjust the optimal detection threshold.