If i'm lucky and someone such as Tinman, Kex, Angelica or some of the other humans were around then they could get me food for me. However at the moment, yes I have to do this all the time.
You could, but you would need to get better at hunting things first. So maybe you can just practise on smaller things for now. Then if they wake up, someone else back at 'camp' could help you hunt bigger things.
No, these are just rabbits. It is a species, like you are a human and i'm a cat. There are others, smaller ones and bigger ones. However with me being the size I am, I can't hunt the bigger ones.