I would like to pose the following question. When wall functions are applied to a turbulent model, does it use both the correlation of the law of the wall and the correlation for the viscous sub layer that y*=U*, or does it used a fudge factor [i.e. damping function such as Van Driest correlation].

Is it normal to use wall functions with lower order models algebraic and first moment closure models, is this due to the fact that lower order models such as k-e are formulated on the assumption of isotropic turbulence

A "wall function" is used to avoid fully resolving the near wall region for turbulent flow which would normally require placing the first grid point deep in the viscous sub-layer. There are a large number of "wall functions". Typically they would evaluate y+ and apply an appropriate treatment based on experimentally based laws plus a bit of numerical treatment depending on the particular turbulence model. It would be normal to apply different treatments if the first grid point is in the viscous sub-layer or outside it. In the context of a wall function I am not sure Van Driest damping deserves the label "fudge factor". The most challenging case for a wall function is not really in or out of the viscous sub-layer but how to handle impinging and separating flows when the experimentally based laws for boundary layers do not really apply. It is normal to use "wall functions" whenever the near wall region is not resolved but this depends to some extent on peoples terminology. The use of "wall functions" is not really dependent on the turbulence model (for RANS predictions - it is a bit different with LES) but the implementation obviously is.