Why do we say, "Who is that man? What does he want", but, "Who is that man? Why is he looking at us". If the second is okay, which I am sure it is, why can't we say, "Who is that man? What is he wanting from us?".
The construction employed in the question is determined by the construction employed in the declarative sentence - the 'answer' you are looking for.
Look is an activity verb, and usually takes the progressive construction in reporting a present action; in a question, subject/auxiliary inversion operates with the existing auxiliary BE:
That man is looking at us. → Why is the man looking at us?
A simple present, That man looks at us, would be unusual, an 'historical present' which ordinarily occurs only in literary or news-reporting contexts.
Want is a stative verb. Such verbs are not usually cast in the progressive†, but in the simple present; since there is no auxiliary, this requires the 'dummy' auxiliary DO for subject/auxiliary inversion in a question:
That man wants something. → What does that man want?
†This does not mean that they may not be cast in the progressive; but when this occurs it usually signals either a different sense or an unusual context which calls for 'recategorization' of the verb.