There are lots of ways to cut and polish an opal, and not all opals are solid stones.
If your stone has a black or dark blue back, and a clear top, it is a triplet. This is made by sandwiching a very thin piece of opal between a solid stone back, often black onyx, and a clear top, either quartz or glass. if you look at your stone from the side, you can see the layers in a triplet.
A doublet lacks the dark back layer, but still has a clear top layer.
The layers in a triplet or doublet are glued together, usually with an epoxy compound, before the stone is cut to shape and polished. These are fairly sturdy, but I still would'nt wash the dishes, or the car while wearing one.
If your stone is solid, it should be translucent, at least in some ares, and possibly even transparent. You may see layers within the stone, usually along planes of "fire" or color.
No opal should be subjected to sudden temperature changes, especially hot or very cold water. If the natural layers and inclusions in the stone change temperature at different rates, the stone may crack.
As to how to mount an opal? Very carefully. I've found bezel setting to be more useful than prong setting. Set in prongs like a diamond raises the stone from the ring, bracelet, etc. and puts it in danger of being knocked about. A bezel, a thin strip of metal pressed about the base of the stone, affords it some protection
Hope this helps.