Yes, Nanami has a girlfriend, although everyone, but Nanami's dad doesn't know that yet. Yes, I think we will get a reveal that Nanami's dad thinks Kaoru is trans
After this chapter, I feel like Kaoru (and Nanami) have far less to worry about the confronting the old man. Sure, it might still be scary for Kaoru, but the dude is more calm and thoughtful than I expected.
At this point, am I right to assume Dad doesn't actually have a problem with his daughter having a guy friend, but he thinks she's too uncomfortable around boys for that to be possible? Even Mom is starting to think she's holding her daughter to an impossible standard.