An interesting question, and one I've thought about a fair bit.
My "main" character, Beatrice Weller, was always largely aromantic - she'd have friends, and people she cared for, but never really had or wanted any particular romantic attachments. She tends towards pansexuality, in the sense that gender - for her - wasn't really a factor in who she found attractive or slept with.
As for her gender, that's a bit more complex. The physical changes in her transformation took hold rather more quickly than anyone anticipated, with the mental/emotional ones taking somewhat longer. Her pronouns at present are interchangeable between 'she/her' and 'it/its', and as she gets further and further from the human woman she used to be, she's increasingly more comfortable with 'it'.
The Aliased Woman saw sexuality, gender, and romance as just more tools to achieve her agenda, even before going completely off the deep end looking for the answer to a question that shouldn't have been asked. So for her, there's no real, genuine feeling or emotional attachment to any of her various partners - just what they can provide her in terms of [insert goal here], and what she offers them in exchange.
As far as her gender goes, while she usually goes with 'she/her' and presents as female, there have been several occasions where, for various reasons (expediency, espionage, etc.) she has used 'he/him' and presented as male. By now, so much of who she was has been stripped away by her search for the Name that even the idea that she should care about gender presentation or sexuality (beyond whatever will get who she's talking to RIGHT NOW to give her what she wants) is an utterly foreign concept to her usual thinking.
The Driven Ascetic is aroace - the trauma of the brutal, horrifying death of her sister in front of her became her entire motive force, propelling what had been a rather soft, indolent girl from her (materially) still comfortable life on the Surface and into the Neath, sharpening herself against every obstacle and speedbump on the way. Genderwise, she goes by 'she' because most people assume she's a 'she/her', and she doesn't give enough of a fuck to comment or notice.
Khalid, meanwhile, presents as entirely masculine, even when he's wearing his Tomb Colonist bandages. He claims to predate most modern notions of sexuality (both in FL's 'now' and our own), and will gleefully engage in polyamorous relationships and casual flings with men, women, Rubberies, Devils, and would probably even hook up with a Curator if he could find one that was interested in humans like that. He'd describe his sexuality as 'enjoying the wonderful buffet of options life serves', though he usually follows that by stating that in Akkadian it flows much better.