In this paper, we study optimal resource allocation strategies for SWIPT focusing on the throughput and energy efficiency of a hybrid system that consists of an energy harvesting unit (EHU) and non-energy harvesting nodes. In addition, we consider an access point (AP) that operates in full duplex mode, i.e., it broadcasts radio frequency signal to power EHU over downlink channel while decoding the information transmitted uplink by the non-harvesting nodes. These nodes send the information-bearing signal to the AP and EHU with non-zero mean. We formulate throughput maximizing optimization problems considering two scenarios for the operation protocol of EHU. In the first scenario, EHU harvests energy but does not decode the information in the received signal. In the second case, EHU is untrusted and it could attempt to eavesdrop the information transmitted by other nodes. In both cases, we derive explicit expressions for the optimal power control policies, and we provide iterative algorithms to obtain the globally optimal solutions. Besides, we formulate an optimization problem that maximizes the system energy efficiency by taking the harvested energy constraint at the EHU into account. For the ease of analysis, we first characterize energy-efficient strategies considering a two-user model, and then generalize to multiple users settings. We also characterize the impact of harvested energy constraint on the optimal system energy efficiency and the significance of introducing non-zero mean input signal on the overall performance. To justify this theoretical framework, we provide simulation results.