What are saturation density and nuclear drip point? What is meant by nuclear saturation density and neutron-drip point? How can we relate the both densities? Where  do these densities occur in the layers of neutron star and  by what reactions a star has to pass to reach at the  neutron-drip point and saturation density?
 A: From scattering experiments, it has been empirically established that the radii of nuclei scale as $A^{1/3}$, where $A$ is the number of nucleons. The nuclear mass of course goes up as $A$ and combining these two leads to a roughly constant nuclear density.This is a consequence of the nature of the residual strong nuclear force, which is attractive at short range, but then becomes strongly repulsive below a certain separation. The position of this minimum in the inter-nucleon potential yields nuclei with a density of $\simeq 2.3 \times 10^{17}$ kg/m$^3$, which is known as the nuclear saturation density.
I am guessing from your question, that the neutron drip point you are interested in is that bulk density inside a neutron star at which it become energetically favourable for neutrons to "leak" out of neutron-rich nuclei in the crust. The neutron drip point needs to be self-consistently calculated by minimising the total energy density of the crust constituents (neutron-rich nuclei, relativistically degenerate electrons and possibly free neutrons) using a model for the mass-energy of a nucleus with arbitrary $A$ and atomic number (like a semi-empirical mass formula) and a model for how any crystalline lattice might change the energy density. The neutron drip point occurs when the Fermi energy of any free neutrons exceeds the neutron rest mass-energy. The canonical work on this was by Baym, Pethick & Sutherland (1971), who put this density at $4.3\times 10^{14}$ kg/m$^3$.
The only (important) connection I see between these two concepts is that of course the nuclear saturation density is determined by the short-range characteristics of the nuclear force, which in turn feeds into the determination of the masses of nuclei. In practice, I suspect that the neutron drip density is not greatly sensitive to this, but it does determine the atomic number and $A$ of the equilibrium nucleus at the density of the neutron drip.
As I mentioned above, the neutron drip occurs in the outer crust of a neutron star, where the composition is still a lattice of (neutron-rich) nuclei, embedded in a sea of relativistic electrons. Travelling inwards towards the neutron star centre, the density rises and the neutron drip density is exceeded. This is still perhaps in the outer $\sim 1$ km of a neutron star. Travelling further inwards, the free neutrons reduce the surface energy term of the existing nuclei and make them less stable. Eventually, at densities of a few $10^{16}$ kg/m$^3$, the nuclear lattice dissolves, possibly passing through several nuclear pasta phases, and at higher densities there is a fluid of neutrons with a small fraction of protons and electrons.
This neutron fluid probably makes up the majority of mass in most neutron stars and is the likely phase of matter up to and beyond the nuclear saturation density.
