Ashutosh’s posts are talking about a specific technical issue in Psi4. I can go into details if you want (dealing with this is on my to-do list!) but the short of it is that our analytic gradient code for conventional integrals cannot handle the frozen core approximation, so frozen core densities aren’t implemented. This is not the case for DF-MP2, which uses DF integrals.
Yes, the default is to use the relaxed OPDM, whether using the properties function or not.
Yes, the frozen core approximation can be used. Orbital relaxation includes the additional frozen core terms, and I’ve personally correctness-tested this. You get exactly the same dipole as if you compute the dipole with a “finite field” approach.