his paper investigates the performance of a full-duplex (FD) uncrewed aerial vehicle (UAV)-assisted energy-harvesting (EH) wireless network, in which a dedicated power beacon supplies radio-frequency energy to both an Internet-of-Things (IoT) sensor node and the UAV relay. A realistic system model is developed by accounting for residual self-interference (RSI), UAV mobility, and three-dimensional deployment. Based on this framework, exact closed-form formulas for the outage probability (OP) and energy efficiency (EE) are derived, enabling a comprehensive assessment of system reliability and energy utilization. The analytical results are validated through Monte-Carlo simulations, demonstrating excellent agreement with numerical results. The results reveal that the OP is highly sensitive to the power beacon transmit power, RSI level, and UAV altitude and horizontal position, where insufficient interference suppression and excessive UAV altitude significantly degrade link reliability. Moreover, the EE exhibits an optimal operating point with respect to the power beacon transmit power. Increasing the number of transmit antennas at the power beacon improves EE, while higher carrier frequencies lead to noticeable performance degradation. These findings provide useful design insights for the deployment and optimization of reliable and energy-efficient UAV-assisted EH networks.