A stone enhancer and sealer will help restore the tile, especially to tile that has faded from the sun. There are a variety of products that are safe for outdoor use at the hardware store.
Dish detergent can leave crystal cloudy - soak the crystal in a 3:1 warm water to vinegar solution to help remove the cloudiness and restore the shine.
Yes it should be okay, depending on what is in the cleanser. Make sure the cleasner does not have any solvents that could cause de-lamination or damage.
Avoid using steel wool or anything similar on your aluminum goods—you may be tempted to scour stuck on food, but doing so could permanently damage the item.
Your dish is probably too thin to immerse vinegar or ammonia. Try using an oven cleaner, WD40, or a metal cleaner first. Follow the instructions on the bottle as much...
