The minimal supersymmetric standard model with a low scale see-saw mechanism is presented. Within this framework, the lepton flavour violation in the charged lepton sector is thoroughly studied. Special attention is paid to the individual loop contributions due to the heavy neutrinos N1,2,3, sneutrinos e N1,2,3 and soft SUSY-breaking terms. For the first time, the complete set of box diagrams is included, in addition to the photon and Z-boson mediated interactions. The complete set of chiral amplitudes and their associate formfactors related to the neutrinoless three-body charged lepton flavor violating decays of the muon and tau, such as µ → eee, τ → µµµ, τ → eµµ and τ → eeµ as well as the coherent µ → e conversion in nuclei, were derived. The obtained analytical results are general and can be applied to most of the New Physics models with charged lepton flavor violation. This systematic analysis has revealed the existence of two new box form factors, which have not been considered before in the existing literature in this area of physics. In the same model, the systematic study of one-loop contributions to the muon anomalous magnetic dipole moment aµ and the electron electric dipole moment de is performed. Special attention is paid to the effect of the sneutrino soft SUSY-breaking parameters, Bv and Av, and their universal CP phases (θ and ϕ) on aµ and de.