1.She looks as if she is sick.(factual-present)
Well, the description of her appearance is factual. We don't know whether she really is sick.
2.She looks as if she were sick.(counterfactual-present)
Given that we are talking about how she appears, I don't think this is possible. She either looks sick or she doesn't. Whether she actually is sick is a different question.
3.She looks as if she had been sick. (counterfactual-past). No.
4.She looks as if she was sick.(factual-past)
Yes, provided we know what past time we are talking about. Otherwise: "She looks as if she has been sick".
If they are correct, I guess the below means "He hadn't been sick, but he only looked so) Am I right? No
5.She looked as if she had been sick.
This means that , at the past time we are talking about, she had the appearance of someone who had previously been sick.
'Look as if' simply describes an appearance. We do not know whether the appearance described reflects the actual situation.
'If' , with 'as', can introduce hypothetical and counterfactual situations.