1." What does he look like?" Correct, asking about his physical appearence
2." What is he like? " （ Is it the same as the first sentence?）Correct, but is asking more about his character or behaviour.
3." How does he look like?" Meaningless, incorrect
4. " How does he look?" Correct, asking about the persons health and how it manifests itself in his appearence. So he might look "tired", "white faced", "shattered" etc
5." How is he like?" Meaningless, incorrect
6. “He has the same weight as me?“ This is not a question, if you want a question it would be "Is he the same weight as me?" generally English relies on the structure to form the sentence. Some versions use the rising inflection, but, that just sounds childish to other English speakers so best avoided.
Can you help?Thanks!