Are you trying to make this a playable civ, or an enemy/trading civ?
If playable, you will need a slew of custom reactions. CAN_STONE is fairly limited in what it allows to be made from stone, and it needs to be stone that accepts edges, and it only works for weapons. Stone armor will require custom reactions. Many of the hardcoded reactions are keyed to the METAL, LEATHER, BONE, WOOD, and STONE tags and can't be easily circumnavigated.
If it is an enemy civ, then the answers are thus:
1) The CAN_STONE tag will not do what you want AFAIK. Material is determined from reaction, but the game is weird about objects vs. object materials.
2) Yes. Custom reactions to make stone, ceramic, or bone equipment is easy. Well, except for gloves. The problem is you will have a hard time picking materials. You either need a reaction for each specific type of stone, or a generic reaction that will grab stones at random. You can make sure it excludes flux stones using the noneconomic token.
You should note that stone and bone are very crappy armor and weapon materials.
3) The easiest way to make sure a civ can't siege with metal weapons or armor is to insure that the civ has absolutely no access to metal (no smelter and no smelter reactions), otherwise it will use those metals. Unfortunately the game doesn't seem to recognize custom reactions that make equipment from new materials, and will not equip attackers with exotic things like bone swords.
Another round-about way is to use the WOOD_WEAPONS and WOOD_ARMOR tokens in the entity file for that civ, which will restrict then to wood equipment. Make sure the entity file does not have INDOOR_WOOD or OUTDOOR_WOOD, and then create new reactions for the entity that give them wood from custom trees you create. Call the tree something like "stone" or "bone", and then the civ will use "stone" and "bone" wood equipment based on the only wood they have access too, the wood from those reactions. Give the tree structural material the material properties you want for the equipment (you could just copy and paste from stone and bone if you wish).