Past statements by justices most certainly can be used to call for a judge to excuse themselves from a case.
Yes, so she should recuse herself from every case involving women's rights.
The definition of a woman has long been a legal position. It's how we determine things like consent. The judge may one day be required to rule on something like a 16 year old wanting to become emancipated. If she confines her answer to a simple answer she could get called on that later.
Actually, the age of consent laws rarely use the term "woman." Mainly they define the victims of non consensual acts that are non-consensual due to the age of the victim, rather than any resistance or expressed lack of consent. They usually call the victim "the child," not "the person who is not a woman," or some such.
But your point is well taken, that the judge likely meant to say that she doesn't know the legal definition if there is one and that if the USSC were to decide on one, the input of biologists would be obtained (it wouldn't, but whatevs).
Look, the judge made a gaffe. She had to switch back and forth from being spoon-fed heavily scripted questions from her fellow Democrats to being asked real questions by the Reps, and she got rattled. No big deal . . . if the Dems/Media hadn't made it one.
She could have released a statement shortly after the day's questioning to this effect:
Of course I know the definition of "woman," in the common usage. I expected legalistic questions and so I gave a legalistic answer that I could have answered more simply and correctly by stating the commonly accepted dictionary definition, which is "an adult female human being."
She could have then plausibly blamed the GOP for asking such a silly question, if she had treated it as such.
She may well have intended to do that, as she walked out of the hearing room that day. But she was pre-empted by her fellow Democratic activists, especially in the media, who immediately jumped on the "no one can define 'a woman'" bandwagon. So we had the sorry spectacle of other administration nominees and officials being asked to define "a woman," and giving answers like, "I'm looking at one."
That is what made it so absurd and turned a relatively harmless and silly gaffe into the entire Democratic Party once again looking like weirdos to normal people.