Same situation but reversed again. If a 13 year old girl engaged, willingly, in sex with an adult man, no matter the situation, you and tons of other people would probably be crying foul that he used his authority over her to coerce her into the act and she was just too scared and that's why she was "willing."
It doesn't matter what you think, a 13 year old can't consent to sex, let alone consent to sex with an adult, let alone an adult with authority over them. The law is pretty clear, and she is 100% a sex offender, no matter if he was technically the one that initiated it or not.
1) Yes, they are different. Most girls of that age have gone through puberty and technically are ready to bear children.
2) You're implying that women don't engage in sex for the sole purpose of enjoyment.
3) You're implying that men can't be raped because they have to get a boner and that boner somehow magically is the only form of consent needed.
You live in a pretty delusional world. Literally everything you said is wrong.