The answer to most of these questions can be found in the CAESAR II Technical Reference Guide, p6-16, Modeling Friction Effects. Pay particular attention to the conclusions here.

As to suggestions for setting the "Friction Stiffness", the higher this value the closer you can accurately model "static friction". However, the higher this value, the more susceptable the model is to convergence problems. We have found that the default value (1.0E6 lb/in) is acceptable in most situations.

To further complicate matters, use the [Search] link at the top right of this page to review all the other posts in this Forum on "friction". There is a great deal of information and opinion on this subject. Pay particular attention to the issue of "what is the proper value of mu"?