*whistle* Okay, but for I start let me lay out my ground plan here. The creation of the universe is random, the development of life even more random, and the evolution of true sentience incredibly more random: no creators, no original designer. Each of these events has an infinitesimally small chance of happening, each even more so than the last. All of it is statistically impossible, including and especially us.
Is it weird that I agree that all of your reasoning makes sense except for the groundwork you based it upon? I don't know what to base the 'creation of the universe is random' part on, meaning the spontaneous existence of mass and energy is something that is possible, but subject to a random chance with low odds? I would say that, if you assume there is no omnipotent creator or designer then, as far as we can conclude, energy cannot be created or destroyed, but can merely change forms, and since we are made of matter (a form of energy) and are able to observe plenty of examples of energy then we must conclude that that energy has always existed in one form or another, its existence isn't subject to random chance (This doesn't tell us why it exists, but that it does).
Also, we know that there is lots of observable energy... and a lot of space between the various sized concentrations of it. We can infer that there may be more energy beyond what we are capable of seeing, which is no conclusion but makes it possible. Our universe may be unlimited, or simply to vast for us to comprehend, containing an infinite (or so vast as to be infinite from our perspective) amount of energy (again there is not an answer as 'why' there would be infinite energy, but just as it is eternal, it can be infinite).
In any case, what I am getting at is that if the universe, in this case meaning all existing energy in whatever form it happens to be, is both eternal and infinite, then it is completely irrelevant how unlikely a random event is, or how unlikely a series of unlikely events are. There is no "statistically impossible" it is either impossible given a universal set of laws that govern all energy (lets not even get into why all energy may or may not be subject to some unknown, arbitrary set of laws), in which case it doesn't happen, or else it is possible and it does happen... if it is possible that it does happen, you could say that it is 'statistically improbable' but that doesn't mean that it doesn't happen, it just isn't likely to happen anywhere near you, but given an infinite amount of energy and time it will happen... an infinite number of times... just, you know, a lesser infinite amount of times than the more probable infinite number of events (if that is worth trying to comprehend in anything more than an academic sense
).
Furthermore, even if we don't assume that energy is both infinite and eternal (because it may not be), but that it is still possible that there is still the possibility that it is incomprehensibly old and incomprehensibly vast then even if you still can't call something that is possible 'statistically impossible' because a vast enough number of events will make an unlikely event occur eventually anyways.
Which isn't to say the cliche "Anything's possible" (Because it is certainly possible that not everything is possible
) but that, if it is possible through random chance, then given enough chances you don't have to worry about 'statistically impossible' because it'll eventually happen anyways.
Beyond this, I won't go to the trouble with each species of saying of saying
"Well, it is theoretically possible that an Andalite exists, but it would have to be beyond our limited knowledge of what physiologically impossible. But while it is theoretically possible it is unlikely because its energy absorption of crushed grass through the hooves is unlikely to be able to provide enough energy for what we know to be required for a creature of roughly its size and nature; so it is either impossible, or simply far beyond what we know to be physiologically possible... but if it is physiologically possible then given a big enough universe it has happened." Suffice it to say that I agree with a lot of the general ideas that RYTX and most others have shared on which creatures we are more likely to come across if we find a faster-than-light method of travel that makes distance irrelevant in the search for extra-terrestrial life.
Following the discussion on "Habitable Zones" and the make-ups of various creatures in the Ani-verse (such as the assumption that a Taxxon is physiologically similar to Earth insects because its outer appearance is similar in shape to a particular Earth insect), I think the larger problem that is too easily overlooked is the likely-hood life exists in the sameway across various planets... all animals have the same structure to their DNA, are carbon-based and require the exact same limited set of nutrients and can survive in environments providing very similar proportions of atmospheric components and pressures: If there was life on the planet you discovered then their food was nutritious to you, or at least safe (you might not be able to consume it, but it wasn't poisonous) the air was breathable, ect. There were never intelligent species of such a different atomic make-up that they simply couldn't exist in our world (other than the water-air barrier), a drug that worked on one specie might be more or less effective than another (unless like the oatmeal it was a single, isolated plot device) but would never simply not work or have a completely different effect. Andalites never wondered "Can we eat this, it sure looks like our grass but is it at all the same" it just simply worked. Ultimately, the biggest problem with the various aliens in the Ani-verse may not be that they are too fantastically alien to be possible, but that they are too not-alien to be probable (Although yes, before you spit my words at me, given a vast enough universe, then eventually a few dozen species that all look very alien but have identical living conditions will eventually develop in relatively near locations).