Ghost in the Shell: Innocence uses some brilliantly subtle visual cues easy to miss if you don't pay close attention. For example, though it's not relevant to the plot, you can tell that Dr. Haraway is a cyborg at a single glance, since she's sitting in a cold room where Togusa has to wrap his coat tight and his breathing becomes visible while wearing a labcoat with sleeves rolled up and top button open from her shirt without signs of discomfort - and her breathing, as well as Batou's, is not visible.
The intro to the 1995 animated film features the Major's body being manufactured in a factory. Or at least, we're led to assume that is what we are seeing. Much of the film's themes center on the Major's sense of self and humanity, and one scene prominently features her encountering a doppelganger of herself in passing. It's entirely possible that the intro didn't feature her at all, establishing the film's theme of human vs machine.
On the page for the original film, the Fantastic Nuke listing talks about the fact that computer programmers are as tightly restricted as nuclear weaponry. This is easily understandable when someone like the Puppetmaster could take over people's brains. None of the people it takes over are important but when you think about it, it's both Fridge Brilliance and Fridge Horror when you realize they could just as easily hack politicians, government agents, generals, admirals, anyone who would have power to use real nukes...
If the Major is a cyborg with a machine body and a human brain, how can she have periods?
They are a reoccurring mental pattern? I mean, she can't really have them due to her artificial body but her brain remembers having those and it might be calming in a paradoxical way.
Alternately, she doesn't have periods, and her claim of being on her period in the first film was just some dry humor.
In most (all?) of the continuities, the Major has been a full cyborg since before puberty, so she wouldn't remember having periods because she never experienced them. On the other hand, unlike many of the other full or partial cyborgs, aside from the dataport on her neck the Major's body is indistinguishable from a normal baseline human. If she wasn't joking, it's possible that her body is programmed to intentionally replicate having a period so she can feel more human.