Optical wireless communication (OWC) over atmospheric turbulence and pointing errors is a well-studied topic. Still, there is limited research on signal fading due to random fog in an outdoor environment for terrestrial wireless communications. In this paper, we analyze the performance of a decode-and-forward (DF) relaying under the combined effect of random fog, pointing errors, and atmospheric turbulence with a negligible line-of-sight (LOS) direct link. We consider a generalized model for the end-to-end channel with independent and not identically distributed (i.ni.d.) pointing errors, random fog with Gamma distributed attenuation coefficient, double generalized gamma (DGG) atmospheric turbulence, and asymmetrical distance between the source and destination. We develop density and distribution functions of signal-to-noise ratio (SNR) under the combined effect of random fog, pointing errors, and atmospheric turbulence (FPT) channel and distribution function for the combined channel with random fog and pointing errors (FP). Using the derived statistical results, we present analytical expressions of the outage probability, average SNR, ergodic rate, and average bit error rate (BER) for both FP and FPT channels in terms of OWC system parameters. We also develop simplified and asymptotic performance analysis to provide insight on the system behavior analytically under various practically relevant scenarios. We demonstrate the mutual effects of channel impairments and pointing errors on the OWC performance, and show that the relaying system provides significant performance improvement compared with the direct transmissions, especially when pointing errors and fog becomes more pronounced.