  The fastest and heaviest pulsar, PSR J0952-0607, with a mass of
$M=2.35\pm0.17 \ M_\odot$, has recently been discovered in the disk of the
Milky Way Galaxy. In response to this discovery, a new RMF model, `NITR' has
been developed. The NITR model's naturalness has been confirmed by assessing
its validity for various finite nuclei and nuclear matter properties, including
incompressibility, symmetry energy, and slope parameter values of 225.11,
31.69, and 43.86 MeV, respectively. These values satisfy the
empirical/experimental limits currently available. The maximum mass and
canonical radius of a neutron star (NS) calculated using the NITR model
parameters are 2.355 $M_\odot$ and 13.13 km, respectively, which fall within
the range of PSR J0952-0607 and the latest NICER limit. This study aims to test
the consistency of the NITR model by applying it to various systems. As a
result, its validity is extensively calibrated, and all the nuclear matter and
NS properties of the NITR model are compared with two established models such
as IOPB-I and FSUGarnet. In addition, the NITR model equation of state (EOS) is
employed to obtain the properties of a dark matter admixed NS (DMANS) using two
approaches (I) single-fluid and (II) two-fluid approaches. In both cases, the
EOS becomes softer due to DM interactions, which reduces various macroscopic
properties such as maximum mass, radius, tidal deformability, etc. The various
observational data such as NICER and HESS are used to constrain the amount of
DM in both cases. Moreover, we discuss the impact of dark matter (DM) on the
nonradial $f$-mode frequency of the NS in a single fluid case only and try to
constrain the amount of DM using different theoretical limits available in the
literature.
