I'd use a word other than "instinct" for those hard-wired things. I remember an article Nathaniel Branden wrote many years ago in The Objectivist where he discredited "instinct" as an unfounded claim for knowledge without any perceptual base. There are reflexes, like all infants have a sucking reflex. There may be a crow reflex that translates the image of large animals into the hormonal fight or flight physiology.
Regarding the crows, I was trying to indicate that they organize the percepts of different animals into different categories, such that the count of four men walking past, plus four deer, just a moment later, (assuming the deer don't trigger any fear reactions), that the count would still be four. Those crows have done something equivalent to taking the percept of each man, 'abstracting' in effect the key similarities while tossing out irrelevant differences so that each man is given a count of 1 and the deer get a count of zero.
You said, "...there is no need for deliberate mental counting (as with symbols, or speech, or holding one's fingers out). The crow does not need to view each man as a "unit" -- because each man is fully remembered as a proper noun. The crow's short-term memory is limited but might exceed that of humans..."
Yes, I agree, but notice that they do recognize the man as danger-creature, but the deer as a not-danger-creature and this very much like our concept formation process.
I'm suspecting that there is a level of conceptual behavior that other animals engage in, but that is different from ours by not having the same kind of self-awareness, agent type of volition, or the depth of abstraction (symbolic, for example, where we can say, "Let x stand for..."), or creative imagination like ours that projects a different thing in the future than we have in the present or have seen in the past.
You wrote, "In play with my dogs (decades ago), I discovered that, with very short term learning (measured in only minutes) it took 2-4 repeats of altered signaling behavior from me before I would get the appropriately-altered response back from them." This is another aspect of learning we don't talk about much, but we all know of. This is where we learn something more fundamental first, and it then becomes a platform, in effect, to learn new things, or variations on older things. The first thing your dogs had to learn was this relationship where you acted in some way that they were supposed to respond to. Then, when they learn that when you behave in this way, and they do the right behavior, they get a treat. That becomes the base and it makes it very fast for them to see that there is a new trick they should do, and their focus narrows down to understanding what is it you want with this new trick signal.
We don't think of babies or even toddlers of being rational, but on one level they are struggling with the most fundamental concepts - learning, at a basic level, things like that there is an external world, that they can be effected by it, that it has a permanence, that they can effect it, that it is made of different things, and so forth. Until those are solidly in place as a foundation (even though they aren't yet, and maybe never will be, conscious of them explicitly, or self-conscious of their presence), they can't go forward with what we usually think of as rational. Babies and toddlers are learning to use the rational faculties. Your dogs had to grasp that they needed to do something, that it was associated with the specific signal you were making.
You wrote, "What folks need to keep in mind is how unique we all are, when compared to everything else in the known universe. True.... but the fact that we can do what we do, is evidence that is is something that can exist, and therefore other entities could be discovered or created that duplicate what now seems to be irrevocably unique.