  We study equal and unequal-mass neutron star mergers by means of new
numerical relativity simulations in which the general relativistic
hydrodynamics solver employs an algorithm that guarantees mass conservation
across the refinement levels of the computational mesh. We consider eight
binary configurations with total mass $M=2.7\,M_\odot$, mass-ratios $q=1$ and
$q=1.16$, and four different equation of states (EOSs), and one configuration
with a stiff EOS, $M=2.5M_\odot$ and $q=1.5$. We focus on the post-merger
dynamics and study the merger remnant, dynamical ejecta and the postmerger
gravitational wave spectrum. Although most of the merger remnants form a
hypermassive neutron star collapsing to a black hole+disk system on dynamical
timescales, stiff EOSs can eventually produce a stable massive neutron star.
Ejecta are mostly emitted around the orbital plane; favored by large mass
ratios and softer EOS. The postmerger wave spectrum is mainly characterized by
non-axisymmetric oscillations of the remnant. The stiff EOS configuration
consisting of a $1.5M_\odot$ and a $1.0M_\odot$ neutron star shows a rather
peculiar dynamics. During merger the companion star is very deformed;
about~$\sim0.03M_\odot$ of rest-mass becomes unbound from the tidal tail due
torque; and the merger remnant forms stable neutron star surrounded by a
massive accretion disk $\sim0.3M_\odot$. Similar configurations might be
particularly interesting for electromagnetic counterparts. Comparing results
obtained with and without the conservative mesh refinement algorithm, we find
that post-merger simulations can be affected by systematic errors if mass
conservation is not enforced in the mesh refinement strategy. However, mass
conservation also depends on grid details and on the artificial atmosphere
setup. [abridged]
