control birth

Birth control vaccines don't exist, but you can get birth control shots.

Yes, you can. While birth control is reliable, there is no birth control that is 100% effective.

Her activism in support of birth control was the reason she was controversial.

Birth control is what is used to prevent unintended pregnancy, there are multiple different types of birth control that work in different ways, it is ignorant to say 'birth control' to mean one specific type of birth control. Without knowing what type of birth control you're referring to we cannot answer your question - some birth control does absolutely nothing to your hormones, some birth control completely shuts down your hormones.