I've read that diamonds are created at a depth of about 180 km. By volcanic activity it comes above. But did plants and trees of 300 million years ago sink so deep? Or is it possible that inorganic carbon, what was already in the Earth, is the source of diamonds?
I've heard also that there could be other exo-planets in the galaxy that are made of diamonds so it looks like it should be possible, or isn't that true?
Diamond isn't made of organic C at all. Organic matter would rather become oil, gas, coal or dissolve entirely.
C itself isn't very common in earth's mantle, but subducted eclogites and peridotites can lead to the needed C-accumulation.
But also meteorite impacts can lead to the genesis of so called micro-diamonds due to the very short lasting but extreme conditions.
Diamond's genesis takes place in depths from 150 up to 700km and at temperatures about 1200-1400°C. Those conditions were present in the upper mantle during the archaeum and hadeum, that's why mining takes places mainly in older crustal zones.
You are right that volcanic activity brings diamond up to the crust and surface of the earth. This process is thought to take only some minutes... This is a very quick process so that the diamond crystal structure won't change back to graphite and it's also the reason many diamond deposits can be found in sediments.
I think that should answer your question. I don't know about the diamond exoplanets, though I've heard of it.. I'd say the process that leads to this is pretty unclear, but perhaps someone has clearer thoughts or information on this.
Not so fast, we can't say that 'no diamond is made of organic carbon'. There are two types of diamond, based upon the relative abundance of $^{12}C$ and $^{13}C$ isotopes. The 'lighter' carbon (relatively $^{13}C$ depleted) are thought to arise from crustal carbon-bearing rocks, possibly including some organic carbon, that was subducted into the mantle, recrystallised at great depth and ultra high pressure, and subsequently brought to the surface, either in kimberlites or in eclogites (as in the small eclogite diamonds around Malmo in Norway). These are the 'eclogite diamonds'. There are also 'heavy carbon' diamonds which are primordial in origin, in which the carbon never left the mantle until spewed up, also in kimberlites.
BTW, the deepest known origin for diamonds is under Brazil, from a depth of 800 km, but Lew is right in that the majority of diamonds are from lesser depths, if you can regard >150 km as a 'lesser depth'.
But did plants and trees of 300 million years ago sink so deep?
300 million years ago (Carboniferous) was a time when large amount of organic carbon was buried to a depth of several kilometres and formed large beds of coal. The pressure and temperature was only moderate (which is why you have coal and not diamonds).
Diamonds form at depths of hundreds of kilometres, and the source of the carbon can be any carbon. Inorganic carbon that was just there in the mantle, or organic carbon that came from any time in the Earth's history, not necessarily from the Carboniferous. So how do you get organic material hundreds of kilometres deep? The answer is subduction. I recommend you view this short video that does a terrific job in explaining of some of this stuff works:
http://www.youtube.com/watch?v=6wJBOk9xjto
there could be other exo-planets in the galaxy that are made of diamonds...
Not quite. Not "made of diamonds". Just planets that have a lot of carbon. In our Earth and the other rocky planets in our solar system there is a lot of oxygen. When you take oxygen and bond it with other elements (silicon, magnesium, iron, aluminium, etc) you end up having rocks. What would happen if a planet would have more carbon than oxygen? In that case, it would be carbon bonding to the elements, not oxygen. You would have rocks made out of carbides, instead of rocks composed of oxides. You probably know carbides: these are usually very strong materials and they are used in industry whenever you need to do hard mechanical stuff.
Anyway, what would happen if you had more carbon than needed to bond with everything else? In that case you would have free carbon that in certain depths in that specific planet would be just in the right condition to form diamond. But this diamond will most likely be mixed together with all of the other carbides so I'm not sure if you will have huge blocks of pure diamond. But who knows?
Some more reading in this article.
To make it even more difficult, recent research revealed existence of microdiamonds. Tiny diamonds (microscopic) were discovered inside kyanite or garnet within granulite rocks. So our explanation for diamond formation is at least partially wrong (they form at much lower pressure then anticipated) or we have some problems with understanding of granulites and subduction mechanisms - can we drag a granulite precursor 150+ km into the mantle without melting it? See one of the recent papers. You can also check some less scientific diamond overview.
