What is the function of the threaded stud with the allen wrench fitting at the top of the struts, the one with the big nut on it? Does turning it have an effect on the workings of the strut, like for example adjusting the dampening?

 

The allen head permits the installer to prevent the strut from rotating while the nut is torqued. In a conventional strut, it has nothing to do with adjusting the dampening.