The DNA part is actually never directly stated - the only thing that comes close is Jake mentioning Na'vi DNA, but he doesn't exactly know much there, but even if they don't use the same base pairs as humans, there would still be something that works in the same way. There would most likely be another structure that works almost identically, but with different bases and possibly different amino acids.
Back onto the taxonomy though, the one for the Na'vi hugely annoys me and I really hope it gets changed, because they are clearly not part of the same family as humans, they have entirely separate evolutionary origins.
As for the avatars, there is an enzyme (NVtranscriptase) which is used to create sequences of Na'vi genetic code from human DNA.
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