Replying to this post because I can’t reblog answers to asks. I’m not exactly a biologist either, but I like this sort of discussion, so I’ll share some of my theories.
I agree with you that Anteverse biology may well be very different from Earth biology. Kaiju may not have a sex binary or sexual reproduction. They probably also don’t fit in our existing biological taxonomy, especially since the novelization throws them completely out of our existing schemes by saying that they’re silicon-based (page 85, possibly some other pages too).
But I’ll take it one step further. The Kaiju may not even be able to reproduce on their own. Travis Beacham states that the Kaiju are built from tissues, which means that some or all of the Kaiju are artificially created and then placed in an environment where they can grow (possibly the uterus of a full-grown Kaiju, as we saw with Otachi, but there are other options).
When I first saw the scene where Newton talks about the Kaiju all having the same DNA, I immediately thought that the differences between them could be due to carefully controlled epigenetics (changing how DNA gets used by cells without changing the DNA). In that case, each Kaiju cell would contain all the genes for all the parts of a Kaiju, which means that Kaiju could reproduce on their own if they had full reproductive systems (nothing in the movie shows that they can produce embryos to gestate on their own, but nothing rules it out).
But all we can actually be sure of is that some of the tissues have the same DNA (Newton’s samples are from the same organ in two different Kaiju) and that some part of the Kaiju DNA is read by the Breach. We don’t know if all the DNA in every single part of a Kaiju is identical across all Kaiju. This opens the possibility that the Kaiju are chimeras created with different DNA for different sets of tissues (and at least one common set that’s read by the Breach). In chimeric organisms with full reproductive systems, the reproductive cells don’t have all the genes needed to create the whole organism. This would pose problems for Kaiju reproduction even if they did have full reproductive systems. Some of the tissues could have very different genes, especially given the great variety of parts and adaptations we see in the Kaiju (which is even worse with sexual reproduction because of genetic recombination, which probably won’t preserve the sets of genes needed for each part).
None of this rules out Kaiju breeding on their own, but it shows that we can’t be sure that it’s possible even though we clearly see a pregnant Kaiju in the movie.