Thank you for your interest in this topic! The anisotropic dielectric properties do have actual results in reality. And I also did some study with the polymer material. I think it is interesting and worthy of a good understanding.
For the first questions you have, dielectric constant is another term of the relative static permittivity. Actually, the more appropriate name should be the relative static permittivity.
For the second questions you have, I think they are related by the following equation,
(1)
\begin{align} \epsilon_{r}=1+\frac{Np}{\epsilon_{0}E} \end{align}
Here, p is the dipole moments. However, the things that are confusing me is, it is a simple summation of the dipole moments and gives the macroscopic dielectric constant. Actually, the summation of all the dipoles is a complicated behavior. For example, there is saturation of dipole polarization. And there are cooperative interactions among the dipole polarization.
These are just my own understandings, I hope they are helpful and welcome for more discussions!
