In an era marked by massive connectivity and a growing number of connected devices, we have gained unprecedented access to a wealth of information, enhancing the reliability and precision of intelligent systems and enabling the de-velopment of learning algorithms that are more capable than ever. However, this proliferation of data also introduces new challenges for centralized learning algorithms for the training and inference processes of these intelligent systems due to increased traffic loads and the necessity of substantial computational resources. Consequently, the introduction of federated learning (FL) and distributed inference systems has become essential. Both FL and distributed inference necessitate communication within the network, specifically, the transmission of model updates and intermediate features. This has led to a significant emphasis on their utilization over wireless channels, underscoring the pivotal role of wireless communications in this context. In pursuit of a practical implementation of federated learning over wireless fading channels, we direct our focus towards cost-effective solutions, accounting for hardware-induced distortions. We consider a blind transmitter scenario, wherein distributed workers operate without access to channel state information (CSI). Meanwhile, the parameter server (PS) employs multiple antennas to align received signals. To mitigate the increased power consumption and hardware cost, we leverage complex-valued, low-resolution digital-to-analog converters (DACs) at the transmitter and analog-to-digital converters (ADCs) at the PS. Through a combination of theoretical analysis and numerical demonstrations, we establish that federated learning systems can effectively operate over fading channels, even in the presence of low-resolution ADCs and DACs. As another aspect of practical implementation, we investigate federated learning with over-the-air aggregation over time-varying wireless channels. In this scenario, workers transmit their local gradients over channels that undergo time variations, stemming from factors such as worker or PS mobility and other transmission medium fluctuations. These channel variations introduce inter-carrier interference (ICI), which can notably degrade the system performance, particularly in cases of rapidly varying channels. We examine the effects of the channel time variations on FL with over-the-air aggregation, and show that the resulting undesired interference terms have only limited destructive effects, which do not prevent the convergence of the distributed learning algorithm. Focusing on the distributed inference concept, we also consider a multi-sensor wireless inference system. In this configuration, several sensors with constrained computational capacities observe common phenomena and engage in collaborative inference efforts alongside a central device. Given the inherent limitations on the computational capabilities of the sensors, the features extracted from the front part of the network are transmitted to an edge device, which necessitates sensor fusion for the intermediate features. We propose Lp-norm inspired and LogSumExp approximations for the maximum operation as a sensor fusion method, resulting in the acquisition of transformation-invariant features that also enable bandwidth-efficient feature transmission. As a further enhancement of the proposed method, we introduce a learnable sensor fusion technique inspired by the Lp-norm. This technique incorporates a trainable parameter, providing the flexibility to customize the sensor fusion according to the unique network and sensor distribution characteristics. We show that by encompassing a spectrum of behaviors, this approach enhances the adaptability of the system and contributes to its overall performance improvement.