Neutrino-nucleus reaction processes play important roles in the synthesis of Li-7, B-11, La-138, Ta-180 and other elements in explosive environments realized in supernovae. We have constructed new shell-model Hamiltonians based on recent progress in the physics of exotic nuclei. The shell evolutions toward drip-lines and the spin responses of nuclei are found to be remarkably improved by the new Hamiltonians. Proper tensor components in the Hamiltonians are shown to be important for the improvements. We then applied these Hamiltonians to calculate the neutrino-nucleus reaction cross sections, and obtained more precise theoretical estimates of supernova nucleosynthesis of Li-7, B-11 and Mn-55 etc, including the neutrino processes. Finally, we propose a new method for determining the neutrino oscillation parameter, the mixing angle theta(13), and the mass hierarchy, by making use of the strong dependence of the yields of Li-7 and B-11 on these parameters.