Yes, during the Prologue, you can choose her sexuality.
Bear in mind that the game is focused on male-female sexuality. So being a lesbian won't keep her away from men
No, unfortunately not. I'd recommend using the website: https://blue-swallow.pages.dev/
Act 3 missing? We're only in Act I in the game so far, so what's Act III?
You should be able to download and play through the zip file. There are 'too many files' (read: art assets) to play through itch, so if you'd like to play in-browser, please go to our website:
https://blue-swallow.pages.dev/
There are definite improvements to be made here. At the current point, sexuality defines the gender of a few different partners for Claire (bisexual/lesbian are female, straight are male), and there are a few mentions of overall reaction to situations based on sexuality, but as you mentioned it definitely needs to be enhanced.
This is known, just requires time and effort (and a lot of careful writing!)
The choices for partners are random and always include potential partners of all genders, simply due to the fact that even people fully straight or gay might still hook up with people outside of their typical 'preference'.