Yes your liver does heel itself. In fact your whole body has this great ability to fix itself. When people have liver transplants, only a small part of the liver is replaced, the liver will grow and regenerate itself completely.
Yes, it is probably like anything else to, more likely the younger you are the more likely your liver would be able to regenerate and heal itself. If you are not too young, it would be more likely you would need a liver transplant. I think as everyone has mentioned, if the liver is past the point of no return, regeneration is not going to help it.