1. JKR never said that trans women are all predators. She said that male predators can falsely claim to be trans to get access to vulnerable women, ie in prison. There have been some instances of male rapists who claimed to be trans in order to get transferred to a woman's prison. They're not actually trans. So JKR isn't actually anti-trans when she's against this, she has said she supports actual trans people (although I think she's become very bitter towards trans *activism* because of how she's been targeted).
I don't believe this problem is anywhere near as widespread as JKR thinks, I think she's been sucked into the radfem conspiracy network. It's not like women can't be rapists. There are female rapists already in prison. And as for the whole bathroom debate, a rapist isn't going to care about the sign on a door, so I think it's a ridiculous argument that men are going to pretend to be trans women to get into bathrooms.
2. JKR also didn't say that trans men are all confused. She said that there's a huge discrepancy between the number of AFAB people identifying as trans men, and AMAB people identifying as trans women. Like orders of magnitude more young AFAB people identifying as trans men, than AMAB identifying as trans women (despite trans women being more represented positively in the media and having more rep in the LGBTQ community). And you would expect to see a similar number of both. So either there's something about being AFAB that makes you more likely to be a trans man (genetically), or there's higher cultural stigma against being a trans woman that prevents AMAB people from coming out to the extent AFAB people are - or as JKR thinks, a big percentage of these AFAB people are not actually trans men but women who want to opt out of being a woman due to oppression.
Again the argument is not against trans men existing, it's arguing that there is a high number of people who think they are trans but aren't actually trans. I would agree with you that it's not JKR's job to diagnose anyone's gender or gatekeep who is or isn't trans. That's up to them and if they want, their doctor/therapist.
3. I don't think it's fair to imply that anyone who feels ambivalent about their gender (especially due to sexism) is not that gender themselves. I know quite a few women who are frustrated with being female because they have endometriosis, because they hate having periods, because they hate being physically shorter/weaker than most men etc. But that doesn't mean they think they're trans either. Not that it would be wrong if they did.
4. As for how I feel about gender - I think it is performative, and that anyone can be any gender they want. Womanhood and manhood is collective and archetypal, there is no one way of being either. No one way of feeling your gender either. So however you want to be, however you want to become, it's your life, your body, your choice, your experience. Do what makes you happy, and I'll respect it, so long as you don't hurt others. Gender is a construct but that doesn't make it not real.
It's ironic that JKR doesn't realise that. She was the one who wrote "Of course it's all in your head, but why would that mean it's not real?"
That's what gender is, I feel.