There are infinitely many possible answers that depend on the relative shapes and sizes of the diamonds.
Three diamonds arranged in a line can form the shape of a triangle.
a cube
Sorry I don't think it makes one
no
yes ithink
Diamonds can be cut into almost any shape.
Do you mean diamonds as in diamond rings, or as in a pack of cards? If the crystal version, then you can't do anything with them other than by grinding bits off to change the shape.
Herkimer "diamonds" are twinned quartz crystals and so could be recognised by crystal shape alone. also, diamonds superior hardness would make it stand out from a Herkimer "diamond" if you were to test the two against a beryl or corundum crystal.
Octahedron
no
As found in their natural state, any
No, they are typically shaped like diamonds.
quadrilateral(squares,rectangles,diamonds,etc.)