1) "I lived in London..." and "I have lived in London..." are both correct sentences but they mean different things. What do you think could be the difference?
2) We don't say, "I want you to back," because "back" isn't a verb in this sentence. It's an adjective. Someone is back when they have returned (from wherever they have been). "I want you back" means the same as "I want you to have returned". (But the latter is very unnatural.)
Student or Learner