None of it happened for me I was induced at 39 weeks
At 38 weeks I dilated one cm and went like that until 40+4 weeks when I went into labor. And even if you lose your mucus plug now it can grow back. Stay patient. I know it's hard to do when your so close to being done but your baby will come when he or she is ready.
Well I will be 39 weeks tomorrow and I am not showing any signs at all. I even had a sweat at 38 weeks and was not dilated at all. I have had 2 other girls and they have all come 2 weeks late and I have always been induced so I am worried that I will have to be induced.
So the answer is they come when ready and in my case they don't want to leave. I would try to be patient as much as possible and it will happen when it should