It is possible that the only thing that has been officially confirmed on EN (as of this question) is that Ace had a girlfriend at one point, and that Lilia loved both Maleanor (proposing to her as a child) and Raverne–that is all!
Anything beyond this gets into speculation and theory, But Cater certainly seems interesting!
*Note: Cater’s literal compliment of Trey (seen above) is very difficult to translate into English, and is not actually the word “handsome.” He is complimenting Trey for having a nice face and a cool smile, but trying to write it out literally becomes very odd in English. He is complimenting Trey for being attractive
Cater does flirt with Trey during Playfulland, and it was not the first time!
Cater talks about dancing with Trey at Kalim’s house and Trey is apparently such a common subject of Cater’s Magicam account that he is teased for it by others.
Cater also compliments Trey during Firelit Sky (Trey stands awkwardly in the background, at first, apparently watching and listening as Malleus complimented Cater).
And Cater’s flirting doesn’t end with Trey! Epel’s labwear vignette involves Cater trying to get Epel to start a Magicam account, inviting him to Mostro Lounge and even following him to the library when Epel turns him down for at least the third time.
There is also the phone-buying date that he invites the gender-unspecified prefect out on in Book 1 and him telling Vil that he thinks he might want to date him, as you say!
Cater also references girls possibly more than any other character:
He talks to Trey about how beautiful he imagines Epel’s sister would be (if he had one), and then jokes about being attracted to Epel’s mother, instead.
He also asks Ace to teach him a party trick “that’ll impress the ladies,” says he is in his element when it is time to “woo a cutie” (in reference to Eliza), comments on the beauty of talking portrait Rosaria, and more.
And, like many of the characters, it might be best not to take what Cater says at face value!
There is a lot more going on with him that appearances betray, with his flirtatiousness possibly being a buffer to keep others away, as he “doesn’t do long-term friends or found family.”
He might be intentionally keeping his relationships surface-level: hence his apparent shallowness!
And Cater isn’t the only one who seems to have intentionally vague characterization in that area, with the first-year students discussing romance together in Ace’s Phantom Bride vignette, and all of them (outside of Ace) failing to specify any preferred gender.
To answer the initial question, I am not sure that we can say any character’s sexuality is one thing or another, and I also think this is by design!
Is Cater actually attracted to most people that he meets, or is he putting on an act as a part of the traveling circus show that is his life?
Is he sincerely interested in Trey, or does he only use compliments as a way to tease him, as he knows that Trey can be particularly sensitive to embarrassing situations? Did he really want to go home with him for winter break, or did he just want to get away from his sisters?
Is he actually interested in Epel, or does he simply want to use Epel’s appearance as a way to boost his own Magicam presence, much like he seems to be trying with Vil?
Is he actually interested in Rosaria, or does he simply want to use her position as a portrait outside of the teacher’s room to his own advantage, like in his school uniform vignette?
Does he actually find things as cute as he says he does, or does he only say “cute” as often as he does as a reflex, due to the environment in which he was raised (as he explains in his labwear vignette)? It is interesting to think about.
Twisted Wonderland Reference Note 