Can I calculate Permittivity and Permeability from S parameters which were measured with a VNA in a log Magnitude format?
Yes this is possible. Take a look at : Dielectric Characterization and Reference Materials by G. Geyer
Yes. It's possible. You need to apply retrieve method , which can help you receive Effective dielectric permittivity and Effective permeability. This is a wideband method, but suffers from an intrinsic limitation related to the electrical thickness of the measured material. Full description of this method available here : https://www.researchgate.net/publication/254018808_A_Stepwise_Nicolson-Ross-Weir-Based_Material_Parameter_Extraction_Method
the answer is yes..but you must better specify your test setup ..it it a coax line (or waveguide)filled with some material sample..there are hundreds of papers on this subject check the author Krupka (via the web or via IEEE explore)..he has written a few nice reviews there