Yes my mother got me one when I was a teenager, I was devastated. When I asked if I could set it free she said it wouldn't be safe. She ended up keeping it until it died many years later.
Thankfully no, not the whole thing. I was vaccinated against rabies and a whole host of other nasties before going on my long Asia and South America trips but I didn't need to have any more jabs after that.
Yes. It was not the best experience since I had morning sickness the entire time but at least I was sick in a beautiful place (Mt Desert Island, Maine.)