d_say“Where does he have lunch? (Why don't we use has instead)”
There can be only
one s marker in a verb phrase, and it has to be on the first verb.
Where does he have lunch?
The verb do, if present, carries the marker of the singular, so the verb have cannot also carry it.
He has lunch.
He does have lunch.
Does he have lunch?
He does not have lunch.
You can't put both does and has in the same verb phrase because that would create a verb phrase with two s markers.
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The same is true of all verbs.
He wants lunch.
He does want lunch.
Does he want lunch?
He does not want lunch.
CJ