The animagus spell

Hi, I was wondering if you need your wand to do the animagus spell? If so, how was Black able to transform in azkaban? If not, how was Peter pettigrew not able transform into a rat after lupus made him back into a human? Is it because he used a spell so he couldn't again? If such a spell exist, does that mean there exist a spell so that you can remove the ability to transform transform into an animal? Also does there exist other spells where you don't need your wand? Other than what kids do before they start at school?