Star formation and chemical enrichment histories of galaxies are imprinted in their internal structures of galaxies, i.e., kinematics and elemental abundances of stars within galaxies. We predict the time evolution of internal structures using our cosmological, hydrodynamical simulations with the feedback from active galactic nuclei (AGN). In the simulations, we have applied a new model for the formation of black holes motivated by the first star formation, in contrast to the merging scenario of previous works. Our simulations reproduce the observed cosmic star formation rates, black hole mass-galaxy mass relation, size-mass relation, and mass-metallicity relation of galaxies, and are in better agreement with the observed down-sizing phenomena, namely, the \alpha enhancement of early type galaxies. In massive galaxies, AGN-driven outflows transport metals into the circumgalactic medium and the intergalactic medium, which is important for a large-scale chemical enrichment in the Universe. Stellar metallicity radial gradients dramatically evolve depending on their merging histories, while gas-phase metallicity gradients are more sensitive to the AGN feedback. Both metallicity gradients weakly correlate with galaxy mass. These predictions will be tested with on-going spectral and IFU surveys.