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?".
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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.