  We introduce \texttt{Weakhub}, a novel neutrino microphysics library that
provides opacities and kernels beyond conventional interactions used in the
literature. This library includes neutrino-matter, neutrino-photon, and
neutrino-neutrino interactions, along with corresponding weak and strong
corrections. A full kinematics approach is adopted for the calculations of
$\beta$-processes, incorporating various weak corrections and medium
modifications due to the nuclear equation of state. Calculations of plasma
processes, electron neutrino-antineutrino annihilation, and nuclear
de-excitation are included. We also present the detailed derivations of weak
interactions and the coupling of them to the two-moment based
general-relativistic multi-group radiation transport in the
\texttt{G}eneral-relativistic \texttt{mu}ltigrid \texttt{nu}merical
(\texttt{Gmunu}) code. We compare the neutrino opacity spectra for all
interactions and estimate their contributions at hydrodynamical points in
core-collapse supernova and binary neutron star postmerger remnant, and predict
the effects of improved opacities in comparison to conventional ones for a
binary neutron star postmerger at a specific hydrodynamical point. We test the
implementation of the conventional set of interactions by comparing it to an
open-source neutrino library \texttt{NuLib} in a core-collapse supernova
simulation. We demonstrate good agreement with discrepancies of less than $\sim
10\%$ in luminosity for all neutrino species, while also highlighting the
reasons contributing to the differences. To compare the advanced interactions
to the conventional set in core-collapse supernova modelling, we perform
simulations to analyze their impacts on neutrino signatures, hydrodynamical
behaviors, and shock dynamics, showing significant deviations.
