In order to transmit data and transfer energy to the low-power Internet of Things (IoT) devices, integrated data and energy networking (IDEN) system may be harnessed. In this context, we propose a bitwise end-to-end design for polar coded IDEN systems, where the conventional encoding/decoding, modulation/demodulation, and energy harvesting (EH) modules are replaced by the neural networks (NNs). In this way, the entire system can be treated as an AutoEncoder (AE) and trained in an end-to-end manner. Hence achieving global optimization. Additionally, we improve the common NN-based belief propagation (BP) decoder by adding an extra hypernetwork, which generates the corresponding NN weights for the main network under different number of iterations, thus the adaptability of the receiver architecture can be further enhanced. Our numerical results demonstrate that our BP-based end-to-end design is superior to conventional BP-based counterparts in terms of both the BER and power transfer, but it is inferior to the successive cancellation list (SCL)-based conventional IDEN system, which may be due to the inherent performance gap between the BP and SCL decoders.