This paper considers a downlink single-cell non-orthogonal multiple access (NOMA) network with uniformly deployed users, while a mixed multicast and unicast traffic scenario is taken into account. By guaranteeing the quality of service (QoS) of the multicast traffic, the multicast outage and secrecy unicast throughput performance is evaluated. In particular, two types of partial channel state information (CSI), namely the imperfect CSI and CSI based on second order statistics (SOS), are investigated in the analytical framework. For both two cases, the closed-form approximations for the multicast outage probability and secrecy unicast throughput are derived except that the approximation for the secrecy unicast throughput in SOS-based CSI only concerns two users. As to the multicast outage probability, the simulation results demonstrate that the NOMA scheme considered in both two cases achieves superior performance compared to the traditional orthogonal multiple access (OMA) scheme, while for the secrecy unicast throughput, the NOMA scheme shows great advantages over the OMA scheme in good condition (high signal-to-noise ratio (SNR)), but is inferior to the OMA scheme in poor condition (low SNR). Moreover, both two cases achieve similar performance except that the NOMA scheme with imperfect CSI obtains larger secrecy unicast throughput than that based on SOS under high SNR condition. Finally, the provided numerical results also confirm that the derived approximations of both two cases for the multicast outage probability and secrecy unicast throughput match well with the Monte Carlo simulations.