`Particle Cosmology and Phenomenology - Related aspects of D3/D7 mu-Split SUSY' Abstract: I discuss a phenomenological N=1 supergravity model and its local type IIB string-theoretic realization involving a space-time filling D3-brane and fluxed stacks of D7-branes wrapping a four-cycle in the large volume limit of a Swiss-Cheese Calabi-Yau which naturally realizes a scenario involving heavy sleptons, squarks, Higgsino, gauginos and neutralinos and the LSP - gravitino - along with one light Higgs and leptons and quarks; this is referred to as D3/D7 mu-Split-Like SUSY. Arguments are given in favor of the gravitino being a viable DM candidate consistent with BBN constraints and yielding the correct relic abundance (assuming a non-thermal production). We also show the possibility of generating electron/neutron EDMs at one- and two-loop levels consistent with experimental expectations in the same setup.