I’ll do my best.
Do you agree that 'being a man or being a woman is a matter of how you feel inside, and physical sex is irrelevant'?
I would agree with the first part of this statement, but not the second. For the majority of people physical sex is strongly
predictive of how they feel inside/ gender identity (sometimes called “subconscious sex”). For a small minority of people gender identity is not predicted by physical sex. We don’t yet know why, although there is lots of interesting research looking into this.
If 'being a woman' is sort of to do with being female, but sort of isn't - can you outline the criteria for being a woman? What exactly do you, personally, mean when you say 'woman'?
I don’t think I can outline the criteria for being a woman. People and bodies are so varied and complex: there are so many different ways of being a woman. However, acknowledging gender is complex and not easily defined , is not the same as saying it’s not real or it doesn’t exist. Gender permeates every aspect of human society. When we make judgements about gender, physical bodies, gender expression, gender roles, (and even sometimes sexuality!) play a role. Gender is not reducible to any one of these things, nor is it entirely separate from them.
in the same way, biological sex itself is now understood to have multiple components. For most people , karyotype (xx, xy) will determine sex development. So it would be ridiculous to say that karyotype is irrelevant or has nothing to do with biological sex. However, we now know that biological sex isn’t definitively determined by karotyope, and cannot be reduced to this measure alone.