1) My sex isn't part of my identity anymore than my hair color or height. I'm a woman because I was born female. I'm happy with my body the way it is but don't feel a need to 'perform' femininity.

I'd argue that most animals don't have a sense of "gender identity" - they certainly don't feel emotional distress at being neutered or have any attachment to their bits. My sister's cat had to have his penis amputated & urethra widened (too much scar tissue from repeated bladder crystals) and essentially his bits look like a female cat's now - and he does not care. He's just happy that he can pee without pain. Most human men would probably be upset at having their penis removed and want reconstructive surgery following amputation. Cats don't care.

1. Sex is not assigned in the vast majority of cases, its observed. The term "assigned sex" was originally meant for intersex people who had indeterminate genitalia at birth and were surgically "made" into whatever the surgeon thought would be easiest - turns out this was a horrible idea. Nowadays more accurate medical testing can allow for the real sex to be actually determined.

2. You are born in the body you are born in. You may not like it, but that's the way it is. I don't think there is any such thing as souls that are somehow put in your body or any of that nonsense. Your brain is part of your body and your body influences your brain. You are your body, not a separate entity.

3. I wouldn't say that gender identity doesn't exist, its just that for many people gender is not an important part of who they are. Most people don't spend a lot of time contemplating how what they like/wear/do aligns with what they think their gender should be. I don't like the term cis because I don't identify as a woman, I am a woman because I have a female body.