Fossilization can occur using literally any mineral that is water soluble, which nearly all of them are. The problem you are running into is "fossil" covers a huge range of things, from insects in amber to shell casts, to permineralized dinosaur bones, the chemistry of the processes therefore also cover a huge range of things and will require quite a solid understanding of geochemistry. Worse, the early stages of fossilization are not well understood. By its nature, figuring out what is and is not in the process of becoming a fossil is difficult, so there are several competing ideas and all of them might well be true.
A few quick definitions.
Stone is any solid composed of nonliving material with a fairly well defined chemical composition, stone is one of the broadest definitions in science.
There is a free textbook on paleontology online, that should be a good spot to get started.
Introduction to Paleobiology and the Fossil Record, Michael J Benton and David A. T. Harper, Wiley-Blackwell.