Heat and light stones would probably fall under the control of both Crystal and Stone Toa. They are both a type of crystal, which is a type of stone.
Not really. The problem with "Stone" is that it is a collection of materials sticking together, whilst "Crystal" is a certain shape in which a material can occur. Stones can be sedimentary (basically, compacted earth or seabeds turned into stone - causing overlap with Toas of Earth), or a conglemarate of several minerals. Even though minerals are crystalline in nature, they don't always occur as actual crystals. In short, stones are absolutey not crystals. They do contain crystals, and a lot of crystalline material, but they are by no means crystal shaped.Sand is, for all intents and purposes, stone. Stone which has been reduced to really really really tiny bits. Although it does contain quartz crystals, it also contains many more materials besides, part of them crystallic in shape, part of them not.
A lightstone is not a stone at all. From my recollection of a lightstone, it is a single material which has a very distinct crystal facing (those perfect shapes along which crystals break). Therefore, by it's very definition, it is a mineral, not a stone.