Your first point is not the only way, and not an approach I'd choose to take. You can confirm if it's sapphire crystal vs mineral using the water drop method. Place a single drop of water on the crystal. If the drop remains spherical when it moves around, then it's sapphire. If it spreads and runs (i.e., gets longer), it's mineral.The only way I know is to see what will scratch it. Sapphire known as corundum can only scratched by something harder like diamonds or as hard like rubies and sapphires which are both corundum just slightly different composition. Diamonds are a 10 on the hardness scale and corundum is a 9. Mineral crystals are softer so they can be scratched by softer material. Lots of quartz which is like a high 7 to low 8 on the hardness scale. The clarity of sapphire crystals compared to mineral crystals are night and day.
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