The MUSE Deep Lensed Field on the Hubble Frontier Field MACS~J0416
  Context: A census of faint and tiny star forming complexes at high redshift
is key to improving our understanding of reionizing sources, galaxy growth and
the formation of globular clusters. Aims: We present the MUSE Deep Lensed Field
(MDLF) program. Methods: We describe Deep MUSE observations of 17.1 hours
integration on a single pointing over the Hubble Frontier Field galaxy cluster
MACS~J0416. Results: We confirm spectroscopic redshifts for all 136 multiple
images of 48 source galaxies at 0.9<z<6.2. Within those galaxies, we securely
identify 182 multiple images of 66 galaxy components that we use to constrain
our lens model. We identify 116 clumps belonging to background high-z galaxies;
the majority of them are multiple images and span magnitude, size and redshift
intervals of [-18,-10], [~400-3] parsec and 1<z<6.6, respectively, with the
most magnified ones probing possible single gravitationally bound star
clusters. The depth of the MDLF combined with lensing magnification lead us to
reach a detection limit for unresolved emission lines of a few 10$^{-20}$
erg/s/cm2, after correction for lensing magnification. Ultraviolet
high-ionization metal lines (and HeII1640) are detected with S/N>10 for
individual objects down to de-lensed magnitude 28-30 suggesting that they are
common in such faint sources. Conclusions:Deep MUSE observations, in
combination with existing HST imaging, allowed us to:(1) confirm redshifts for
extremely faint high-z sources;(2) peer into their internal clumps (down to
100-200 pc scale);(3) in some cases break down such clumps into bound star
clusters (<20 pc scale);(4) double the number of constraints for the lens
model,reaching an unprecedented set of 182 bona-fide multiple images and
confirming up to 213 galaxy cluster members. These results demonstrate the
power that JWST and future ELTs will have when combined to study gravitational
telescopes.[abridged]
