  We investigate the nuclear symmetry energy and neutron star properties using
a Bayesian analysis based on constraints from different chiral effective field
theory calculations using new energy density functionals that allow for large
variations at high densities. Constraints at high densities are included from
observations of GW170817 and from NICER. In particular, we show that both NICER
analyses lead to very similar posterior results for the symmetry energy and
neutron star properties when folded into our equation-of-state framework. Using
the posteriors, we provide results for the symmetry energy and the slope
parameter, as well as for the proton fraction, the speed of sound, and the
central density in neutron stars. Moreover, we explore correlations of neutron
star radii with the pressure and the speed of sound in neutron stars. Our 95\%
credibility ranges for the symmetry energy $S_v$, the slope parameter $L$, and
the radius of a 1.4$\msun$ neutron star, $R_{1.4}$, are
$S_v=(30.6\text{--}33.9)$\,MeV, $L=(43.7\text{--}70.0)$\,MeV, and
$R_{1.4}=(11.6\text{--}13.2)$\,km. Our analysis for the proton fraction shows
that larger and/or heavier neutron stars are more likely to cool rapidly via
the direct Urca process. Within our equation-of-state framework a maximum mass
of neutron stars $M_{\rm max}>2.1\msun$ indicates that the speed of sound needs
to exceed the conformal limit.
