"I'm not liked" means that someone or some people or something (like a dog or cat or pet) does not like you, but it is unclear who it is who does not like you. You must say who or what does not like you. "Nobody likes me" means that everyone/everybody who knows you does not like you (but "everyone and everybody only refers to humans and does not refer to dogs and cats and pets.

Yeap, they mean the same thing but there must be a good reason to make the sentence "I am not liked". "Nobody likes me" is more often...

Yes.