As a biologist, I’d be fascinated to know how God had originally intended for humans to reproduce in an asexual manner.
We cannot be too sure. The Fathers only denied that this would have been sexual reproduction involving the genitalia, but never gave an affirmative answer to how humans would multiply without sexual reproduction.
Is genetic diversity also a result of the fall?
Possibly so. It could be that the human acquisition of genetics was part of the “garments of skin” in which Adam and Eve were clothed after their expulsion from the Garden. The Patristic interpretation of that verse was that we were given animalistic natures for the new fallen and carnal life which we had acquired through the fall. For contrast, we see that Christ after the Resurrection, though still being a material being, clearly did not possess such an animalistic nature, as he was able to perform acts (such as passing through walls, appearing suddenly from nowhere, etc.), which are not natural to animals. There was something very otherworldly about his body.
If the Church allows us to believe that God used the process of evolution to create humans, then there’s some…interesting…territory to jump into.
Yes, there is, because it presents an enormous challenge to the patristic notion that there was no death before the fall. I frankly struggle with evolution, because the biological evidence and fossil record seem to make it something which cannot be denied outright, but that is a discussion for another thread.
How much of the gender theology as taught by specific saints is binding to Catholics (or Orthodox in your case)?
For Roman Catholics, I cannot say. For the Orthodox, I cannot really think of what would be particularly binding, except to believe that the two genders differ, and that God intended to create man with genders (i.e., that gender was not a product of the fall, though it is acceptable to believe as St. Maximus did that genders were created because God foresaw the fall).
What’s the Orthodox position on “deep-seated homosexual tendencies” and “reparative therapy”?
Orthodoxy regards “deep-seated homosexual tendencies” as a passion (as all inclinations towards sin are) which needs to be uprooted, so that the sexual urges do not control the life of whoever might be so unfortunate to suffer under such a spiritual affliction. The calling in such cases would certainly be to live chastely (though if one were capable of getting married, that would also be a possibility). On reparative therapies, I do not know. I know many who are suspicious of them, especially because they do not reflect the Orthodox view of sexuality as being a product of the fall; rather they would try to encourage one not to conquer his sexual passions, but to redirect them to another outlet (in this case, the opposite sex), a solution which would be inferior to living chastely and uprooting the passion altogether.