{\it Effect of peculiar motion in weak lensing:} I will present the effect of peculiar motion in weak gravitational lensing. More precisely, I will show that the cosmic shear and the convergence, evaluated in a perturbed Friedmann Universe, contain a new contribution related to galaxies' peculiar velocities. This contribution does not affect cosmic shear in a measurable way, since it is of second order in the velocity. However, its effect on the convergence is important, especially for redshifts $z < 1$. As a consequence, peculiar motion modifies also the relation between the shear and the convergence. \medskip {\it Neutralino dark matter annihilation in the first stars:} Within the framework of a LCDM Universe, the first generation of stars to form (Population III.1) has very peculiar characteristics. Recent studies show that their astrophysical peculiarities may also enhance the effects of WIMP dark matter annihilation on their birth and life. I will describe the physical mechanisms by means of which this happens, and their effects on the stellar properties. I will also briefly comment on how the effects on stellar populations could be possibly used as astrophysical experiments for constraining DM properties.