  XO-2 is the first confirmed wide stellar binary system where the almost twin
components XO-2N and XO-2S have planets. This stimulated a detailed
characterization study of the stellar and planetary components based on new
observations. We collected high-resolution spectra with the HARPS-N
spectrograph and multi-band light curves. Spectral analysis led to an accurate
determination of the stellar atmospheric parameters and characterization of the
stellar activity. We collected 14 transit light curves of XO-2Nb used to
improve the transit parameters. Photometry provided accurate magnitude
differences between the stars and a measure of their rotation periods. The iron
abundance of XO-2N was found to be +0.054 dex greater, within more than
3-sigma, than that of XO-2S. We confirm a long-term variation in the radial
velocities of XO-2N, and we detected a turn-over with respect to previous
measurements. We suggest the presence of a second massive companion in an outer
orbit or the stellar activity cycle as possible causes of the observed
acceleration. The latter explanation seems more plausible with the present
dataset. We obtained an accurate value of the projected spin-orbit angle for
the XO-2N system (lambda=7+/-11 degrees), and estimated the real 3-D spin-orbit
angle (psi=27 +12/-27 degrees). We measured the XO-2 rotation periods, and
found a value of P=41.6 days in the case of XO-2N, in excellent agreement with
the predictions. The period of XO-2S appears shorter, with an ambiguity between
26 and 34.5 days that we cannot solve with the present dataset alone. XO-2N
appears to be more active than the companion, and this could be due to the fact
that we sampled different phases of their activity cycle, or to an interaction
between XO-2N and its hot Jupiter that we could not confirm.
