Are kidney stones formed in response to a viral infection? If so, in what percent of cases?

This is true 100% across the board for all forms of kidney stones that an underlying chronic viral presence is a precipitating factor. There are associated phenomena, both genetic and functional from dietary considerations, and in some cases other disease states contributing to the vulnerability of some individuals to become stone formers, while others harboring the same virus might not. But in all instances, it is a virus that triggers the start of the problem and without the viral presence it would not take place.