Your tips for telling a rock from a fossil are great. I also tell new collectors to look for symmetry. Any shape that you see alongside a mirror image of itself could be a fossil. Bilateral symmetry is just one kind. There is also radial symmetry like you see on a cross-section of many round fossils like crinoid stems and echinoids. Symmetry can be found in natural geological processes as well but most forms of life have it so it always deserves a close examination.