Well the mineral Tanzanite, a the blue/purple variety of the mineral zoisite, discovered in the Meralani (Merelani) Hills of Northern Tanzania in 1967, is very beautiful and as it is ONLY found in this one place (and the deposit is running out), it could be regarded as the most rare gemstone mineral.
However, you could argue that the blue 'Hope' diamond or a large pink diamond is the rarest and most beautiful mineral.
Gem or Gemstones.
crystals
When a mineral is rare to locate, it is typically referred to as a "rare mineral" or "rare earth mineral." These minerals are not readily abundant in the Earth's crust and can be challenging to find and extract.
gems
A rare mineral that can be cut and polished could be called a gemstone.
Natural Pink Topaz is considered to be the most rare because it is found in natural beautiful colors are rare to the species and it is very costly also.
Coal is not a mineral and is not rare.
yes but a very rare mineral
yes but a very rare mineral
Fluorite is not that rare but the purer forms referred to as "acid grade" are and most comes from China. It is required for manufacturing of fluorinated products such as PTFE
Yes.
diamond because it is a native crystalline carbon that is the hardest known mineral