Does Yoda have DNA

Or critical thoughts on evolution. If DNA encodes amino acids, which encode proteins, which build all manners of structures, a reasonable questions is ‘what all can actually be built with this DNA?’ Could an extraterrestrial being use the same encodings as earth’s evolutionary tree or are there very clear limits to the kind of structures possible without going outside of our 4 bits of code? A case in point is evolution which presents us with a vast array of life-forms, albeit ever so slightly in a discontinuous fashion. There are lots of different dogs, for instance, but no cat-dog. We find fossils of birds that look a bit like reptiles, and such, but we do not have a phylogenetic tree in all its shades, as far as I know. The point is, given any particular species, there are only so many mutations possible on that particular genome, many of them lethal, some intraspecies variations, some leading to a new species. While we can easily say that there is a path from dinosaurs to birds, as it is a fait accompli, the question is, can we define possible paths without relying on hindsight, or in other words, can we emulate DNA algorithmically? And if so, will our models show that there are only a fairly limited number of possible developments, meaning evolution was almost bound to come up with what we perceive, or will there be a virtual infinity of possible creations, making our particular manifestations a sort of accident.
It seems at first thought, that the latter hypothesis ought to be the correct one, as there are so many combinations possible of the base-pairs, and hence the aminoacids encoded by them. But then, a tremendous amount of combinations is probably meaningless in terms of proteins created. Also, the DNA is not at all like a blueprint, a miniature replica of the organism in encoded form, but rather like a program, a small number of instructions without a one-to-one correspondence to their output. So, while Yoda is by all appearances a close relative of humans, breathing air of roughly the same composition, having muscles, bones, eyes, a brain, bilateral symmetry, a skin and digestive tract, he may be one of those outputs that is not obtainable from the available nucleotides. I believe the situation is analogous to mathematics, or formal logic, where a given set of theorems can only produce a certain set of statements and not others, even though they all look plausible.
A fantastic limit of this scenario would be where only one very finite set of organisms could be produced, namely the ones that historically existed on earth. In this case, there is no real evolution. Related to this idea is the one where no smooth transitions exist and species are like crystal lattices of a complex organic salt, that can solidify in a large but distinct number of configurations.
While neither of these scenarios is a proof that there is a creator involved in the process, the discovery of significant limits to the variety of lifeforms that can be encoded via our DNA weighs a bit toward the existence of God, much like a discovery that we are truly alone in the universe, or at least in the galaxy.