1-
Now, now, you are sounding disgeneous
You were the one bringing transition of inorganic matter to organic life in your previous post. That's adressed nowhere in Darwin work. What you were talking was
origin of life not
evolution of species. It only shows that you don't understand what you are talking about and like all creationnists, like to mix things to try to prove your point
Evolution of species as per Darwin (who never talked about how life appeared on Earth and who created it on the contrary to what crreationnists think) is that : In a given population appears all the time variations of physical features (what we call today : phenotype). If this physical features give an advantage in a situation/environment that lasts, it allows a better survivability of the individuals bearing it so a better chance to reproduce and pass down those advantages to the offspring. This physical feature then spread in the population, giving it ultimately divergent enough of the original population to obtain a new specie.
The Darwin theory is correct while incomplete because DNA, genetics, mutations and epigenetic were not discovered during his era. It is still however accurate even if it needed to be refined with the molecular biology discoveries.
3- I am not specialist in C14 dating. However
i) if C14 was found in diamonds, it would be atremendous discovery that could be published in a major science article. Which in returns mean accuracy of the work would have been verified. Which is not the case here. I can also tomorrow write an article saying that i have found little grey DNA in a slug and publish it in "Cosmology and Alien Life" or any trash pseudoscience journal. That doesn't make it true. So, yes, to begin with, the discovery itself is questionable
ii) even if it is true they detected C14 in diamonds, the only fact that it is below the treshold admitted as last accurate limit of datation with this isotope (50 000 years but more modern and accurate mass spectrometry systems give a limit of 41 000 to 43 5000 years) should raise en eyebrow in any science man eye. Or in other mean, it screams contamination or calibration issue.
A more detailed lenghty answer by some specialists here :
http://www.talkorigins.org/faqs/rate-critique.html
4-Find me people with all the physical and genetic features of the neanderthal. You'd find none
Some people may have one physical feature that reminds neanderthal (like thick eyebrow bone), that doesn't mean they are of the neanderthalensis specie. Jaguar and Leopard have spots they are not of the same specie
We have enough Neanderthalensis DNA material to classify it as a different specie of Homo. Much like Jaguar and Leopard are different species of the felis branch. First check the definition of what is a specie, that's seems also to be something you are not understanding