will diamond burn as coal does?

It burns, but not exactly like coal. Coal has other elements like H, N, and S. Coal has a variety of hydrocarbon molecules and burns at a lower temperature than diamond.
Diamonds will burn. In fact if the diamond is pure carbon, it will leave no ash, disappearing as CO2 gas. This has been reported by insurance companies after structure fires.

if you get it hot enough. Something like 900 degrees C depending on how much free oxygen is in the system.

NO. Its the hardest material on earth. Mike

Diamonds burn. That is how it was determined that diamonds were made of carbon. After a diamond burns in oxygen, nothing but CO2 remains.

yes

Obviously NOT