Venus' convective cloud layers and associated gravity waves strongly impact the local and global budget of heat, momentum and chemical species. Here we use for the first time three-dimensional turbulence-resolving dynamical integrations of Venus' atmosphere from the surface to 100 km altitude, coupled with fully interactive radiative transfer computations. We show that this enables to correctly reproduce the vertical position (46-55 km altitude) and thickness (9 km) of the main convective cloud layer measured by Venus Express and Akatsuki radio-occultations, as well as the intensity of convective plumes (3 m/s) measured by VeGa balloons. Both the radiative forcing in the visible and the large-scale dynamical impact play a role in the variability of the cloud convective activity with local time and latitude. Our model reproduces the diurnal cycle in cloud convection observed by Akatsuki at the low-latitudes, and the lack thereof observed by Venus Express at the equator. The observed enhancement of cloud convection at high latitudes is simulated by our model, although underestimated compared to observations. We show that the influence of the vertical shear of horizontal super-rotating winds must be accounted for in our model to allow for gravity waves of the observed intensity (> 1 K) and horizontal wavelength (up to 20 km) to be generated through the "obstacle effect" mechanism. The vertical extent of our model also allows us to predict for the first time a 7-km-thick convective layer at the cloud top (70 km altitude) caused by the solar absorption of the unknown UV absorber.