Yes.
Yes.
Not quite monthly, and not a true menstrual cycle, but even some cisfemale (again, this is to clarify and not provoke) healthcare providers have stared at me in disbelief and said "it sounds like you had a period."
It's actually not unusual for this to not be a normal thing for ciswomen, with some not having it at all.
No, but many women for one reason or another can't.
What's this etc and right?
Something that might interest you is I have wondered what my sex chromosomes are and if I might have some weird condition. I don't have an adams apple, my feet and hands are small for someone born male of my height (and indeed Ive met many women with bigger hands and feet the same size), had breast development before hormone treatment, women's clothing fits better, and weird things and other things. I even have the lazy eye passed down on through the women in my mom's family and even have my mom's maternal grandmother looks in the face.