Radio Frequency Energy Harvesting (RF-EH) networks are key enablers of massive Internet-of-things by providing controllable and long-distance energy transfer to energy-limited devices. Relays, helping either energy or information transfer, have been demonstrated to significantly improve the performance of these networks. This paper studies the joint relay selection, scheduling, and power control problem in multiple-source-multiple-relay RF-EH networks under nonlinear EH conditions. We first obtain the optimal solution to the scheduling and power control problem for the given relay selection. Then, the relay selection problem is formulated as a classification problem, for which two convolutional neural network (CNN) based architectures are proposed. While the first architecture employs conventional 2D convolution blocks and benefits from skip connections between layers; the second architecture replaces them with inception blocks, to decrease trainable parameter size without sacrificing accuracy for memory-constrained applications. To decrease the runtime complexity further, teacher-student learning is employed such that the teacher network is larger, and the student is a smaller size CNN-based architecture distilling the teacher's knowledge. A novel dichotomous search-based algorithm is employed to determine the best architecture for the student network. Our simulation results demonstrate that the proposed solutions provide lower complexity than the state-of-art iterative approaches without compromising optimality.