This article develops novel approaches for designing robust transceivers and energy covariance in an IoT network (IoTNe) powered by energy harvesting (EH). Our goal is to minimize the mean square error (mse) at the fusion center (FC) while considering the uncertainty of channel state information (CSI). The proposed designs incorporate both Gaussian and bounded CSI uncertainty models to model the uncertainty in CSI. Furthermore, two different optimal bit allocation schemes have been proposed for quantizing the measurements from each sensor node (SeN). However, solving the resulting mse optimization problems with constraints on individual SeN power and total bit rate proves to be challenging due to their nonconvex nature under both CSI uncertainty models. To address this challenge, we develop a block coordinate descent (BCD)-based iterative framework. This framework leverages the block convexity of the optimization objective and provides efficient solutions for both uncertainty paradigms considered. By making use of this analytical tractability, we obtain improved performance compared with the uncertainty-agnostic scheme that disregards CSI uncertainty. We validate our approach through numerical simulations, which not only support our analytical findings but also demonstrate the superior performance achieved with our method that accounts for CSI uncertainty.