This paper investigates the outage and throughput performance of full-duplex (FD) cooperative relaying (CR) based non-orthogonal multiple access system (NOMA) with energy harvesting (EH) i.e., FD-CR-EH-NOMA system. We consider a network scenario, where the base station (BS) serves two downlink users, with the near user configured as a FD relay to deliver messages to the far user. We derive analytical expressions for the outage probabilities experienced by the users and the system outage probability of FD-CR-EH-NOMA network under time switching relaying (TSR) protocol in the presence/absence of direct link from BS to the far user. Assuming imperfect successive interference cancellation (i-SIC), we derive analytical expressions for (i) optimal power allocation (OPA) factor at the BS and (ii) optimal time switching (OTS) factor at the relay that independently minimizes the system outage probability. Further, we use the alternating optimization technique to determine the jointly optimal power allocation and time switching factors that minimize the system outage probability. Furthermore, we determine the OTS factor that maximizes the asymptotic throughput of the system in the delay-limited transmission mode. With the help of numerical and simulation investigations, we show that the system outage and throughput of the considered network improve significantly under the proposed schemes.