1. Is he like his father?
  2. Does he resemble his father?
    Do both mean same?
  3. Like whom is he?
  4. Is he looking like whom?
    Are these questions correct?

1 and 2 usually mean the same, though sometimes ‘like’ can mean in habit, characteristic, etc. whereas 'resemble; tends to ask about physical attributes.

3 and 4 are incorrect.
Who is he like?
Who does he look like?
He looks like who(m)?