I'm afraid I 'm posting too much these days, but I will try to answer.
The first answer is not. What I see in Modelica.Thermal.Media is a record named MineralOil, not a package extending Modelica.Media.Interfaces.PartialMedium, that is what is needed as medium for the Fluid library.
After this, yes, probably it is possible to build a valid medium package from the data in the MineralOil record. I see that it is a very simple medium, with constant properties for density, specific heats, thermal conductivity and kinematic viscosity. The closest package in the Media library I think that is the TableBased one. In Modelica.Media.Incompressible.Examples there is tha package named Essotherm650 that probably is already good for your tests. If it is not, I would copy this package in myr work, rename it and put the same values at all temperatures. Taking into account that in the record the viscosity is kinematic and in the package  dynamic.
I have not tested it, but I hope that the BasicHX model is compatible with any package derived from partialMedium.