In the tropical ocean, diurnal heating and the formation of atmospheric convection cells associated with local precipitation events, cold pools and wind bursts, have been shown to impact air-sea exchange and the structure of the ocean surface layer. Here, we use a high-resolution regional ocean model, forced by an atmospheric Large Eddy Simulation (LES) that explicitly resolves these processes in a realistic scenario in the tropical north-east Atlantic Ocean, to study their impact on the ocean surface layer and parameterized air-sea fluxes. We find that the oceanic heat loss is, unexpectedly, reduced in the presence of cold pools by on average 30 W m^-2 due to the higher air humidity, weaker mean winds, and increased cloud cover. Our results also show that the total non-solar heat flux is dominated by the diurnal cycle of the trade winds, rather than by diurnal heating. In the ocean surface layer, local wind bursts, rain layers, and cloud shading induce a strong lateral variability in the strength and depth of Diurnal Warm Layers, questioning the local applicability of available bulk parameterizations. From a series of numerical tracer experiments, we identify a new shear-dispersion mechanism, induced by the Diurnal jet, that is reflected in an extreme anisotropy of horizontal dispersion with diffusivities of order 10-100 m² s^-1.