  The iso-electronic $d^{4}$ compounds of the $4d$ series show rich phase
diagrams due to competing spin, charge and orbital degrees of freedom in
presence of strong correlations and structural distortions. One such
iso-electronic series, $Ca_{2-x}Sr_{x}RuO_{4}$, is studied within the GGA (and
spin-orbit coupled GGA) plus DMFT formalism using the hybridization expansion
of continuous time Quantum Monte Carlo solver. While the local dynamical
correlations make $Sr_{2}RuO_{4}$ a Hund's metal, they drive $Ca_{2}RuO_{4}$ to
a Mott insulating ground state. We study the dynamic and static single-particle
and local irreducible vertex-corrected two-particle responses at three
different points ($x = 2.0, 0.5, 0.0$) to understand the anomalous cross-over
from Hund's metal ($x = 2.0 $) to a Mott insulator ($x = 0 $) and find that a
structural distortion is likely to be responsible for the cross-over. Further,
dynamical correlations reveal that the band-width ($W$) of the Hund's metal is
larger than its effective local Hubbard $U$, and a finite Hund's coupling
$J_{H}$ helps it remain in a bad metallic and nearly spin-frozen state over a
large temperature range. $Ca_{2}RuO_{4}$, on the other hand, is intrinsically
driven to the proximity of a Mott transition due to narrowing of band width
($U/W > 1.5$), though its finite temperature excitations indicate bad
metallicity. We show that there is a critical end point of second-order
structural transition at $x = 0.5$, where spin fluctuations become critically
singular and follow the exact scaling of conformally invariant boundary field
theory. The critical end point of quasi-$3D$ nature is associated with an
effective dimensional cross-over between the $x = 2.0$ and $x=0.0$ quasi-$2D$
structures. Finally we draw a modified magnetic phase diagram of the material,
showing a fan-like region starting from the quantum critical end point at $x =
0.5.$
