Dye is most commonly used to colour capes, but they are also used in several quests.
rose red dye and bonemeal
You can craft things with Lapis like: A Lapis Lazuli block, light blue dye, cyan dye, purple dye, magenta dye and blue wool. You can check out Minecraft Wiki for some help and tips.
For colouring wool blocks.
no
No, but you can dye it's collar
Burn cactus in a furnace.
You can dye wool or sheep black with it.
You can't. But with resource packs or mods you can.
You cant unfortunately but there maybe a mod out there.
Burn cactus in a furnace.
Orange dye can be made by putting yellow dye (from crafting yellow flowers) and red dye (from crafting red flowers) on the crafting table.
There is no 'brown dye' - to dye wool brown, you just place it along with Cocoa Beans into your crafting slot, to make Brown Wool.