Rocky planets located in the habitable zones around very low-mass objects are ideal targets for searching for life outside our Solar System. In order to better understand their formation and evolution, N-body simulations are needed. These simulations are developed assuming a star close to the substellar mass limit as the central object. The simulations include tidal and general relativistic effects that incorporate the contraction and evolution of the rotational period of the central object during 100 Myr, as well as interactions of the disk of gas with a sample of protoplanetary embryos during the gas disk lifetime. A very relevant result is that just one of the prescriptions used to treat the interactions between the disk and the sample of embryos allows the survival of a close-in compact planet population of interest, located in the habitable zone of the systems with a wide range of masses from Mars-like up to Earth-like planets and close to orbital period commensurabilities. Moreover, the resulting planets with semi-major axis a < 0.1 au are in agreement with the cumulative distribution of the period ratio of adjacent terrestrial-like exoplanets around stars with masses M < 0.14 Msun (Sanchez et el 2022, https://arxiv.org/pdf/2203). On the other hand, in order to estimate the probability of detection of planetary systems around very low-mass stars, a numerical tool in python was developed. This new tool calculates the changes in stellar flux, radial velocity and proper motion of a sample of stars due to the interaction with their planetary systems. It estimates the probability of detection of planetary systems regarding different samplings and errors associated with a given instrument or survey. A significant result is that the radial velocity method (used by CARMENES) allows a high probability of planetary detection around very low-mass stars (Sanchez et al, in prep).