Ha ha... interesting questions.
Although the right answer is more along the lines of what Dr. Adequate has said... that we don't know.
I'm gonna have a crack at it anyway in the name of fun
Gregory Rogers writes:
Namely: let us hypothesize that there is another extinction event and
man, homo sapiens, under extreme environmental pressures, now begins to adapt or change (mutate).
Let us say, for example, there is a worldwide nuclear war. 90 percent of homo sapiens is wiped out, and the only option is to go miles underground, into deep tunnels and caverns.
To make it interesting, let us say that these caverns have virtually no light, are only three feet high, and that a massive landslide blocks re-entry to the surface.
Fair enough.
First point - Evolution is random with no goal or future-thought. It's quite possible that humans don't get a mutation that's helpful for them soon enough... and we just all die. Horrible, dark, lonely deaths. Such is the fate of 99% of all species that have ever evolved to exist on this planet. They just weren't able to keep up with the change in their environment fast enough and... poof... dead.
But, we're having fun... so let's say we have some sort of food storages and renewable water sources and such that we're able to keep on keeping on and we're protected from the radiation 'cause we're so deep and we get lucky with some useful adaptations and all the weak people die off in a morally-acceptable way such that the new adaptations can flourish in the population.
what direction would the new mutational tendencies take?
Again, evolution doesn't
have a direction. But with natural selection (dark environment, damp soil, filtered air...) we can take some guesses on what sort of possible adaptations might get kept in the population. Again... given that we stop having sex with the peeps who do not have these adaptation 'cause they're holding everyone else back. In a morally-acceptable way, of course
Ultimately legs and arms would grow smaller, he would crawl like a large reptile; he would perhaps develop sonar technique like a bat for sensing direction, and the eyes would fall away almost completely.
You definitely can't use the word "ultimately." There's nothing definitive about evolution.
What if we developed claws and just dug bigger tunnels so that there was no more pressure to be smaller?
What if getting smaller made for smaller lungs and those people all died because they couldn't get enough air through the dirt from the surface?
What if we were to discover a way to create fire again and no longer had pressure to lose our eyes. And, in fact, had pressure to develop even greater eye-sight in low-light conditions?
Maybe what you say would happen.
Maybe not.
It all depends on exactly what the pressures are, if they're constant, if we (as humans who use tools and morality) don't circumvent them in some other way anyway... so many factors.
But, yes. If we're going to treat us surviving humans as "animals" and assume these selection pressures you've described actually exist and have an affect on us... then yes. Given enough time, we would adapt to the environment. Perhaps not in exactly the way you describe, but in some way.
Maybe we don't develop sonar at all. Maybe we develop some kind of temperature-heat-detection-radar that allows us to "see" (sense our environment) using that method. Maybe vision becomes unimportant and we survive just fine feeling our way around in the dark. Maybe we start growing longer and longer hairs/tendrils/whiskers from our body in order to physically sense things before we run into them.
The point is we don't get to choose.
We might not develop anything and die off.
We may develop something... but it's is likely to be something "good enough" instead of something "perfectly right" or "cool."
Further to this, how long might it take before homo sapiens evolves into a whole new organism — i.e., comparable to dinosaurs evolving into birds, which in that case involved scales becoming feathers, a mouth with teeth becoming a beak, wings developing, etc.
About 100 million years.
Not kidding.
All this time, we'll have to stay in the tunnels/underground with the same selection pressures working on us.
In perhaps a different hypothetical instance, how long might it take for human flesh to evolve into another substance — reptilian skin, let us say, or else for arms and hands to become claws, or what have you?
Skin to another substance? 10 million years.
Arms/hands to become claws or 'what-have-you'? 50+ million years.
Breaking it down, how many mutations would be required for such a transition? How long would each mutational change take, and how long would be required altogether for the transition?
Apologies, questions are even above my "for fun" pay-grade
Hope this sheds a little light. And remember... Dr. Adequate's answer is even more right: We don't know.