The only addition I would make is I believe grounds for "gender identity" could be hard coded in us before we are born. So that would make it biological too. It just does not always match the sex of the person.
Cisgender is usually applied to people that identify as male or female and were born with matching sex i.e. a male with a male gender identity or a female with a female gender identity.
I think traits are usually social things. What society says is a masculine thing is what a masculine thing is. These are not universal. They are irrelevant when it comes to gender identity and sex. They are just ways of expression and behaviour.
I think having a non-binary gender identity does not exclude you from conforming to male or female stereotypes. You can identify as non-binary and still behave and look just like a man or woman. I for one only have one gender, it is my own and it is a non-binary one in that I don't identify as a male or female. For me it is not about not conforming, I simply don't understand what it would feel like to be male or female. But really I can't understand why anyone would want to 'act' like male. Though I tend towards feminity myself, I have no idea why. All I can do is act like myself.
What makes you a man is self identification, nothing else. Whether society views you as a man is a different story.
How this all relates to attraction is a bit more complex. I think it is best not to over alalyse attraction and just allow yourself to be attracted to who you are attracted to.
Hope this is helpful.
Nicky