Ooh, a quiz ?
Why are the new euphemisms for 'female'—’bleeder,’ ‘uterus-haver,’ ‘menstruator’—so degrading to women?
Because the TRA movement is led by misogynists?
Why are trans demands so lopsided, with much demanded of women and very little demanded of men?
See above.
Why do ideologically-noncompliant women take so much more heat from trans activists than violent men?
Again, the reasons are rooted in misogyny and a fear of women. As women have gained rights and shown that they are capable of as much as men, those who believe in male superiority have found themselves on shaky ground, so are finding new ways to undermine women. Also, those who believe in gender can't get their conformist heads around the fact that women are supposed to be compliant, and men are supposed to be dominant, but some just aren't. (I didn't say these were sensible reasons - you didn't specify that they had to be, did you?)
Why are we deferring to the gender identity claims of male rapists and serial killers?
Probably a misunderstanding of the situation, in a similar way to how many people fell for the 'no reference to black bin bags or black coffee' nonsense back in the day.
Why are women’s movements being co-opted?
See above - and also jealousy of the way in which female socialisation tends to encourage co-operative behaviour, so we have been more inclined to 'be kind' and made ourselves easy targets. More fool us, but we live and learn.
Does anyone abuse self-id policies?
Are you kidding? Yes - see Chewbacca's post. Oh, but if a female author uses a plot even remotely like the true story in that report she is castigated fro transphobia.
What’s the difference between a ‘transwoman’ and a man who says he’s a woman?
Is that a riddle? Seriously - It's not for me to say, really.
How is it fair for someone like Lia Thomas to demolish women’s swimming records?
This one's easy. It Is Not Fair.
What's the difference between Rachel Dolezal and Caitlyn Jenner?
Erm, were they both mis-assigned at birth in their different ways? Can I have half a point for that, at least? Caitlin Jenner seems to have at least some sensible views on trans issues, though.
What was wrong with what JK Rowling said?
It was read by lots of people, and made them think about the issues surrounding gender issues? It really annoys TRAs when they are asked to explain why she is so evil? Women shouldn't have the financial power to sue men when they defame or otherwise abuse them, as that upsets the natural order of things?