Radiative zone means that energy there is transported by radiation, not by movements of bulk matter. Matter as a whole in the core and the radiative zone does not move. Photons or electromagnetic waves, as you like, transport the energy towards the outer shells. Convective zone means that energy there is transported by convection. That is, large amounts of hot matter cross part of the zone upwards, deliver their energy to the matter they find there and having cooled, plunge back in the inner shell to get heated again. What causes these moves is the buoyancy. The heated matter is less dense and therefore its weight is smaller than that of an equal volume of cooler material. Above the convective zone, energy transport is essentially radiative again, but solar wind and solar flares account for a (probably very small) part.
Energy production takes place in the core. Four hydrogen nuclei (protons) fuse together to make a helium nucleus plus energy. (that's a VERY sketchy description)