The physics of a planar chiral p-wave superconductor is studied for various vortex configurations, and the occurrence of vortex quasi-particle bound states is presented together with their ensuing collective properties, such as sub-gap bands induced by inter-vortex tunneling. To this end, I will first show a general method to diagonalize the Hamiltonian of a superconductor in the presence of a vortex lattice, that employs only smooth gauge transformations. It renders the Hamiltonian to be periodic (thus allowing the use of a Bloch theorem) and enables the treatment of systems with vortices of finite radii. Then I will show how the anomalous charge response, c_xy can be calculated using a modified Streda formula. Interestingly, c_xy is proportional to the anomalous Hall conductivity, which in turn is proportional to the polar Kerr angle. Thus, these results should affect the calculation of the polar Kerr effect, hence they are significant for the determination of the order parameter of superconductors. Remarkably, the results reveal that c_xy is a sum of two contributions, one which is non-universal and the other equals ^κ/_8π, where κ is the Chern number of the superconductor. I will argue that the quantized contribution is due to the formation of vortex bound states.