Hmm. IMO, he sounds sketchy. He claims that he’s asexual, and yet not only does he have a sexual history but also talks about other people around you in a sexual manner? Let me ask (you don’t have to answer if you want to), but do you two engage sexually? If you two still do, then he’s feeding you complete BS on the whole asexual thing. Asexuals don’t go talking about how they want to be sexually involved with people. That goes completely against what asexuality is; having no sexual attraction to anyone. Regardless of if they’re with you or talking about the crush, that doesn’t sound like asexuality if they’re talking about someone sexually.

I would say with the crush thing, to communicate with him about it. Let him know that all the stuff he talks about regarding her sexually and romantically is making you uncomfortable. You’re his partner, and he should know better than to say those things in front of you. But let him know that it makes you uncomfortable. If he dismisses your feelings at all, ex: “Babe, what I’m talking about doesn’t amount to anything, so don’t go stressing about it”, or brings up your past in anyway with the topic if he knows about your rocky past with relationships, I’d say to take your chances and leave this man. But that’s only if those scenarios happen. If he understands and never does it again, then good. But if he downplays it, dismisses your feelings, or uses your past against you, leave that relationship.