On the gem side, the vast majority of people wearing diamonds would tell you they have utility.
On the industrial side, diamond is a fascinating material with physical properties at the extremes, e.g. hardness, thermal conductivity, electrical conductivity, etc etc. It is vital in many applications where there is simply no other material which could fulfil the physical requirements.
Fashions change, yet people believe that diamonds have permanent value ('is forever'). In contrast to bullion, this is relatively recent development with little ties to traditional banking practices.
>>On the industrial side, diamond is a fascinating material
These can be made on demand, and cutting diamonds cost something like $1 per carat. Nobody is raging against the crystal lattice.
No, actually diamonds (and other gems) have had artistic/cultural/symbolic value for as long as civilizations have existed. I.e. the "crown jewels", the "hope diamond" and more: http://en.wikipedia.org/wiki/List_of_diamonds
They simply do wonders with light and are aesthetically pleasing when well cut. Not to mention they are incredibly hard to destroy.
Yes and no. Also the ability to make diamond is pretty recent with a lot of the fundamental research having been funded by De Beers.