rover123 the first sentence of your post provides us with a physical description and formula for turquoise. The formula is irrelevant to the other three semi-precious stones.
Yes, they are all colours and semi-precious stones.
Agates are all forms of chalcedony (fine grained quartz) which are characterised by bands or zones that differ from one another in colour. Chemically, all agates are silicon dioxide.
Topaz is a form of hydrous aluminium fluorosilicate. Garnet is a complex double silicate mineral composed of calcium, manganese, magnesium and ferrous compounds combined with aluminium chromium and ferric ions. Aquamarine is a form of the mineral beryl.