for question 1: When you say "someone is on my case" you are saying that "someone is meddling with my affairs". So in this case, "the whole world is on your case" means "the whole world is looking at you, judging you, and meddling with your everyday life". For question 2: "You ain't seen nothing like me yet" is saying that "there is nothing in this world that is like me (not anyone or anything)".
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