Competition in sports, women's or men's is a privilege not a right, so no, trans people do not have the right to compete in women's sports.
I don't care what bathroom you use as long as you don't commit any crimes in there, and that means not exposing yourself to any women or children you encounter in that restroom.
As for prisons, I think we have enough trans women in prison to give them their own wing.
Rape counselors can be of any sex, men do get raped, but you should have the right to a counselor you feel comfortable with.
Where should men who have been raped go for shelter?
Organs are already being grown, it's only a matter of time before a trans woman can start producing the large immotile gametes.