Periods are a shedding of vaginal lining to combat failed or unfertilized eggs and to refresh the lining for a new egg present only in very few animals native to Earth, a select handful of mammals. If they are so rare on earth I would not find it hard to believe that alien civilizations have never even heard of periods. I'd even dare to say that humans would be considered freaks of nature on the galactic civilization scale for having females who bleed once a month for several days as a normal regular occurrence and would likely be a taboo to even speak about. I'd imagine that some technology would have been made some time ago that stops the less-than-savoury side of periods. Heat is different because it doesn't involve blood and is merely a period of hyper fertility, something that is much more common in the animal kingdom so more likely to be found and less taboo.
If periods were to be a thing then they would only really affect human characters, or they'd affect the character regardless because they will always be at least part human. I'd imagine it would only be an aspect of the player unless a writer and coder puts that feature into a character, and that every month in the game(unless their reproductive facilities have changed for heat or ovi) there'd be periods of infertility where there's no need no worry about pregnancy and then a period of fertility where you'll need to watch out if you don't intend on your character being pregnant. Not that it ever will get in unfiltered, blood in a sexual sense or anywhere near genitals is on the no-no list.
If I got ninja'd, whatevs. TFs will not ever affect combat in TiTS unless it is something like red myr venom, vanae milk, or the cerespirin spore cloud.
