Hold a diamond ring up to your eyes and look though the back light comes through... even when it is cut... however the better the clarity and cut the more light is reflected back at you
Diamonds are transparent, light does pass through . The 'sparkle' is due to the very high refractive index of diamond (the degree to which light is 'bent' on entering and leaving the substance) this gives the sparkle.
More on Diamond and the refeactive index here, Diamond is not 'dense' it has a density of 3.5 so it is 3.5 times as dense as water. Iron as an example has a density of around 7.2 Lead is about 15.