Data collection of amount of residential houses in a designated area

The Overpass API allows you to limit your query to a bounding box, an area already in OpenStreetMap or an arbitrary polygon.

Note that the "completeness" of OpenStreetMap varies by area, and even if the building are traced they may only be tagged generically as building=yes or building=residential rather than as one of the house specific tags (=bungalow, detached, `semidetached_house', etc.).