  We present a detailed mass reconstruction and a novel study on the
substructure properties in the core of the CLASH and Frontier Fields galaxy
cluster MACS J0416.1-2403. We show and employ our extensive spectroscopic data
set taken with the VIMOS instrument as part of our CLASH-VLT program, to
confirm spectroscopically 10 strong lensing systems and to select a sample of
175 plausible cluster members to a limiting stellar mass of log(M_*/M_Sun) ~
8.6. We reproduce the measured positions of 30 multiple images with a
remarkable median offset of only 0.3" by means of a comprehensive strong
lensing model comprised of 2 cluster dark-matter halos, represented by cored
elliptical pseudo-isothermal mass distributions, and the cluster member
components. The latter have total mass-to-light ratios increasing with the
galaxy HST/WFC3 near-IR (F160W) luminosities. The measurement of the total
enclosed mass within the Einstein radius is accurate to ~5%, including
systematic uncertainties. We emphasize that the use of multiple-image systems
with spectroscopic redshifts and knowledge of cluster membership based on
extensive spectroscopic information is key to constructing robust
high-resolution mass maps. We also produce magnification maps over the central
area that is covered with HST observations. We investigate the galaxy
contribution, both in terms of total and stellar mass, to the total mass budget
of the cluster. When compared with the outcomes of cosmological $N$-body
simulations, our results point to a lack of massive subhalos in the inner
regions of simulated clusters with total masses similar to that of MACS
J0416.1-2403. Our findings of the location and shape of the cluster dark-matter
halo density profiles and on the cluster substructures provide intriguing tests
of the assumed collisionless, cold nature of dark matter and of the role played
by baryons in the process of structure formation.
