Never did get to refer to the books but just re-reminded myself of some stuff via Wiki - the amethyst grows in geodes, which usually occur in volcanic rocks (basalt, safe) but can also occur in limestones and other sedimentary rocks. Because I can't quite tell from the picture if your amethyst is grown on limestone, it would be good to test it as limestone could affect your tank's pH. Just put a small drop of vinegar on anything not amethyst (several areas, if there's several different types) and see if it fizzes. If it does, it's limestone. If it doesn't, it may still be another carbonate mineral called dolomite (very similar but more
magnesium) - try taking an old dull steel knife and try to scrape off a bit of the rock material into a powder; if you can't scrape it off it's definitely not dolomite. If you can, put some vinegar on the powder - if that fizzes, it's dolomite. If nothing fizzes it's definitely safe for your aquarium.
Regarding sanding it down: amethyst is quartz, which is a very hard substance. Many sandpapers are made from quartz, and so won't be effective in grinding down the crystal as they're the same stuff - you'd need something harder. Garnet sandpaper MAY work, and if your dremel is made from silicon carbide that may work too. A steel construction file may work too (but they're very similar in hardness so it may damage the file). Otherwise the only option would be to chisel some off, but then you run the risk of breaking the crystal (it will split along a crystal plane, and you'll have two fragments, both with even sharper edges). Good luck
