  Neutrinos emitted in the coalescence of two neutron stars affect the dynamics
of the outflow ejecta and the nucleosynthesis of heavy elements. In this work,
we analyze the neutrino emission properties and the conditions leading to the
growth of flavor instabilities in merger remnants consisting of a hypermassive
neutron star and an accretion disk during the first 10 ms after the merger. The
analyses are based on hydrodynamical simulations that include a modeling of
neutrino emission and absorption effects via the "Improved
Leakage-Equilibration-Absorption Scheme" (ILEAS). We also examine the
nucleosynthesis of the heavy elements via the rapid neutron-capture process
(r-process) inside the material ejected during this phase. The dominant
emission of $\bar\nu_e$ over $\nu_e$ from the merger remnant leads to favorable
conditions for the occurrence of fast pairwise flavor conversions of neutrinos,
independent of the chosen equation of state or the mass ratio of the binary.
The nucleosynthesis outcome is very robust, ranging from the first to the third
r-process peaks. In particular, more than $10^{-5}$ $M_\odot$ of strontium are
produced in these early ejecta that may account for the GW170817 kilonova
observation. We find that the amount of ejecta containing free neutrons after
the $r$-process freeze-out, which may power early-time UV emission, is reduced
by roughly a factor of 10 when compared to simulations that do not include weak
interactions. Finally, the potential flavor equipartition between all neutrino
flavors is mainly found to affect the nucleosynthesis outcome in the polar
ejecta within $\lesssim 30^\circ$, by changing the amount of the produced
iron-peak and first-peak nuclei, but it does not alter the lanthanide mass
fraction therein.
