Soft question here, but I was wondering just what exactly free parameters are? I have a murky understanding on the concept but I would much appreciate someone shedding some light on the matter. Is Newton's gravitational constant $G$ a free parameter of that theory? What exactly are the requirements for a parameter to be considered a free parameter?
Free parameters are not predefined but must be estimated by theory or experimentally. Or it can be a parameter used in fitting a dataset with an expression. The free parameters are varied to get a good fit to the data.
G in Newton's gravitational equation is a free parameter and has been measured but not with high accuracy.