How could Lara have concealed her pregnancy?
Operating under the assumption that the Kryptonian gestation period is long enough that Lara would have had to conceal her condition, how do we explain no one catching the natural birth in progress?
The structure Jor-El and Lara call home is referred to twice in the film as a “citadel” which is another name for a fortress or castle. In other words, something hardened to survive against and through a siege. This suggests that the Citadel is sufficiently self-sustaining that Lara could have carried Kal-El to term without venturing into society which may take issue with her natural birth.
At this time, we don’t know Lara’s function in society or the necessity of her venturing out. We know that Lara has some adeptness with the science of finding a home for Kal-El and in launching his vessel. The ability to telecommute through drones and their Liquid Geo interface, there might be little call for her to leave the Citadel, particularly if her primary occupation was to work with Jor-El. Their relative isolation and autonomy tends to be supported by additional evidence, aside from the birth of Kal-El.
First, their radically different views about Krypton’s fate and where it should go next. Second, the number of novel technologies Jor-El was able to develop in his Citadel. The copy of Jor-El’s consciousness appears to be a novel technology. It is why Zod asks whether the shadow can feel Jor-El’s pain, because the parameters of such technology was not commonplace or known. Kal-El’s vessel, equipped with a precious Phantom Drive during a period of resource scarcity and after Krypton had withdrawn from the stars, was also a private project. That Jor-El was able to work on these without issue or challenge makes having a secret pregnancy plausible.
If natural birth is heresy, why aren’t Kryptonians genetically modified to be sterile?
Value judgment. There is plenty of evidence that Krypton is not a purely utilitarian society. We see many examples of art, design, aesthetics, and so on, exhibiting a soul to Krypton. The Council wears impractical, ornate, and unnecessary accoutrements, the walls bear carvings, sayings, and scripture, and so on. That means that this is a society governed by more than purely the most efficient or effective thing conceivable. That is hardly unthinkable and, in some contexts, admirable. Many conceptions of American Justice uphold principles that are less efficient from a utilitarian perspective, but nonetheless promote the values that our society would like to project and social contract agrees upon. For example, it would be many times more efficient to subject the citizenry to “Guilty until proven innocent”, however, because we uphold values like Blackstone’s formulation, “It is better that ten guilty persons escape than that one innocent suffer” that we afford the accused every presumption of innocence until proven guilty.
Likewise, although the expedient and efficient thing may be to rob Kryptonians of their natural reproductive capability, seeded in Krypton’s values, culture, religion, etc. may be a principle of personal integrity that prevents the State from taking that away. There’s some support for the integrity and perfection of the person being a vaunted value in Zod’s eugenic conception of an ideal Krypton.
Moreover, it is unclear whether the prohibition against Natural Birth is necessarily a strongly held Kryptonian value or if the intensity of that belief is more of Zod’s dogma. While there had been no natural births in centuries and Zod calls it heresy, Jor-El comments that artificial population control was “established” (but not necessarily prescribed by law, religion, or otherwise) and recall that Jor-El was just about to disclose the birth of Kal-El to the Council before Zod interrupted. If the topic was so taboo that no Council member could get over the fact that Jor-El had brought a child into the world naturally, then it is unlikely to have been a talking point in his presentation to them. It is possible that while it was a centuries-old tradition with, in the last days of Krypton, it may only had inertia rather than genuine conviction behind the position against Natural Birth.
A more mechanical answer? Some aspect of their reproductive and genetic manipulative technology requires or benefits from preserving the ability to reproduce.
Why didn’t Jor-El make a copy of Lara’s consciousness too?
As discussed above, Jor-El’s “shadow” or Artificial Intelligence guided by his memories and consciousness and projected in a high fidelity hologram, appears to be a novel technology insofar as Zod having questions about the degree of suffering it can experience. However, neither is Zod completely taken aback by the technology and nor should he be as there are logical precursors extant in the glimpses we see of Kryptonian technology: the interrogation “dream machine” used on Kal-El and Lois and the somatic recondition both indicate that mind-machine interfaces is within the grasp of Kryptonian technology, making just a matter of time to meaningfully record a consciousness and bind it to an artificial intelligence, another technology we know they have to some degree.
However, we know nothing of how this process of meaningfully recording a consciousness works. Is it traumatic, like the dream machine interrogations can be or somatic reconditioning is implied to be? Is it lengthy, like somatic recondition is implied to be? If somatic reconditioning was easy, quick, painless, and guaranteed, it seems like you’d hardly need 300 cycles to accomplish it, manacles, hibernation sarcophagi, and an off-world prison… rather, those all seem like requirements if that mind-machine interface is slow and the subject prone to resistance. We don’t know that the parameters of making a duplicate of your consciousness for this novel technology invented by Jor-El is compatible with a pregnant mother carrying their precious first and only child to term.
I think the most simple answer is that the shadow was an ad hoc measure included under time pressure and other constraints and Lara’s exclusion is more a by-product of circumstance than intention.
However, even if we were to find it intentional, it is not necessarily unreasonable. We know Jor-El specifically intended to limit Krypton’s influence on Kal-El. It is the reason that he and Lara did not join Kal-El on his journey. It is a conviction that he held so strongly that he was willing to die for it. It seems unlikely that he would compromise that belief any further than necessary by introducing another possible influence into Kal-El’s life that might prevent him from serving as the bridge between peoples.