  This work provides an overview of our recent results in studying two most
important and widely discussed quantum processes: electron-positron pairs
production off a probe photon propagating through a polarized short-pulsed
electromagnetic (e.g.\ laser) wave field or generalized Breit-Wheeler process,
and a single a photon emission off an electron interacting with the laser
pules, so-called non-linear Compton scattering. We show that the probabilities
of particle production in both processes are determined by interplay of two
dynamical effects, where the first one is related to the shape and duration of
the pulse and the second one is non-linear dynamics of the interaction of
charged fermions with a strong electromagnetic field. We elaborate suitable
expressions for the production probabilities and cross sections, convenient for
studying evolution of the plasma in presence of strong electromagnetic fields
