We first explore the commonly used moment matching for deriving approximations for generalized fading channels in three different applications - a) We calculate secure outage probability and strictly positive secrecy capacity expressions over $kappa-mu$ shadowed fading channels. b) We derive outage probability (OP) and ergodic rate expressions for the uplink of multi-user massive multi-input multi-output (MIMO) systems with low-resolution analog-to-digital converters. c) We derive approximate OP and rate expressions for systems employing maximum ratio combining (MRC) when both the desired signal and the interfering signals undergo $eta-mu$ fading. Secondly, we determine the approximate symbol error rate and OP expressions when Optimum Combining is employed and when both the user and interferers experience Rician fading. We highlight the complicated nature of these expressions even when the eigenvalue statistics of non-central Wishart distribution is available. For both complex $kappa-mu$ and $eta-mu$ distribution, which do not have any matrix distribution, we propose a Wishart distributed approximation, by minimizing KL divergence. We explore the utility of the matrix approximations in some 5G-relevant applications. Finally, we assume that the user signal and the interferer signals experience $kappa-mu$ shadowed fading and determine the limiting distribution of the maximum and minimum over such random variables. Furthermore, we analyze the utility of the derived asymptotic results in some applications.