Most diamonds are well over 3 billion years old, although the rocks in which they are embedded are much younger; possibly only 50 million years. I say 'most diamonds' because some are younger - they form as a result of meteorite impacts.
Diamonds are embedded in volcanic rocks which are really solidified magma. The diamonds were formed in the earth's mantle, and brought to the surface during periods of intense volcanic activity. The diamond you see sparkling in the jeweller's window was deep in the molten interior of our planet, long before life on earth began.
The objects in the image are galaxies. Our galaxy is the milky way, which is big - a beam of light would take 100,000 years to cross it from side to side, and it contains roughly 200 billion stars. That said, our galaxy is pretty standard by the standards of the known universe - there are billions of other galaxies just like it.
The galaxies in the image are small by comparison - a mere 1000 light years across, but bear in mind that they were then pretty young; only 500 million years old, which is the twinkling of an eye in astronomical time. They were busily creating new stars at around 50 times the rate that the Milky way is doing it now.
By any stretch of the imagination the image is astonishing - we're looking at objects as they were just after the big bang - our solar system didn't even exist then.