Genderqueerness refers to an identification with neither, both or a combination of male and female genders across a spectrum. Genderfluid, androgynous, non-binary and other terms are also used by those who fit this description in some way. Many genderqueer people don't choose to have any type of surgery to alter their physical appearance; many do. Like sexuality, it's a broad and beautiful church.
1. "Are you a boy or a girl?"
My genderqueer partner always uses the simple answer of "yes". I love watching people open and shut their mouths like goldfish when they hear that. "No" or "maybe" also work as responses.
2. "But you look so much like a woman/man."
Being genderqueer doesn't mean presenting or identifying as an exact 50/50 mix of male and female. It just means there's a mix. Also genderfluidity means you may differ from day to day.